@article {lang:finitefields,
    AUTHOR = {Lang, S.},
     TITLE = {Algebraic groups over finite fields},
   JOURNAL = {Amer. J. Math.},
    VOLUME = {78},
      YEAR = {1956},
     PAGES = {555--563},
   MRCLASS = {14.0X},
  MRNUMBER = {19,174a},
MRREVIEWER = {P. Roquette},
}

@article {mccallum:duality,
    AUTHOR = {McCallum, W.\thinspace{}G.},
     TITLE = {Duality theorems for {N}\'eron models},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {53},
      YEAR = {1986},
    NUMBER = {4},
     PAGES = {1093--1124},
      ISSN = {0012-7094},
     CODEN = {DUMJAO},
   MRCLASS = {14K15 (11G10 14F20)},
  MRNUMBER = {88c:14062},
MRREVIEWER = {Gerd Faltings},
}

@article {schneider:iwasawa,
    AUTHOR = {Schneider, P.},
     TITLE = {Iwasawa ${L}$-functions of varieties over algebraic number
              fields. {A} first approach},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {71},
      YEAR = {1983},
    NUMBER = {2},
     PAGES = {251--293},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {11G40 (11G10 14G10 14K15)},
  MRNUMBER = {85d:11063},
MRREVIEWER = {Stephen Lichtenbaum},
}


@article {milne:bsdres,
    AUTHOR = {Milne, J.\thinspace{}S.},
     TITLE = {On the arithmetic of abelian varieties},
   JOURNAL = {Invent. Math.},
    VOLUME = {17},
      YEAR = {1972},
     PAGES = {177--190},
   MRCLASS = {14K15 (14G10 14G25)},
  MRNUMBER = {48 \#8512},
MRREVIEWER = {T. Ono},
}


@incollection {sd:bsd,
    AUTHOR = {Swinnerton-Dyer, P.},
     TITLE = {The conjectures of {B}irch and {S}winnerton-{D}yer, and of
              {T}ate},
 BOOKTITLE = {Proc. Conf. Local Fields (Driebergen, 1966)},
     PAGES = {132--157},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {1967},
   MRCLASS = {14.48},
  MRNUMBER = {37 \#6287},
MRREVIEWER = {Y. Nakai},
}

@book {MR37:3885,
     TITLE = {Proceedings of a {C}onference on {L}ocal {F}ields},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1967},
     PAGES = {v+214},
   MRCLASS = {00.04 (12.00)},
  MRNUMBER = {37 \#3885},
}

@article {jordan-livne:sha,
    AUTHOR = {Jordan, B.\thinspace{}W. and Livn{\'e}, R.},
     TITLE = {On {A}tkin-{L}ehner quotients of {S}himura curves},
   JOURNAL = {Bull. London Math. Soc.},
  FJOURNAL = {The Bulletin of the London Mathematical Society},
    VOLUME = {31},
      YEAR = {1999},
    NUMBER = {6},
     PAGES = {681--685},
      ISSN = {0024-6093},
     CODEN = {LMSBBT},
   MRCLASS = {11G18 (11G10 14G35)},
  MRNUMBER = {2000j:11090},
MRREVIEWER = {Chandrashekhar Khare},
}

@incollection {rubin:kato,
    AUTHOR = {Rubin, K.},
     TITLE = {Euler systems and modular elliptic curves},
 BOOKTITLE = {Galois representations in arithmetic algebraic geometry
              (Durham, 1996)},
     PAGES = {351--367},
 PUBLISHER = {Cambridge Univ. Press},
   ADDRESS = {Cambridge},
      YEAR = {1998},
   MRCLASS = {11G40 (11G05 11R18 11R23)},
  MRNUMBER = {2001a:11106},
MRREVIEWER = {Massimo Bertolini},
}

@book {MR2000a:11005,
     TITLE = {Galois representations in arithmetic algebraic geometry},
    EDITOR = {Scholl, A. J. and Taylor, R. L.},
      NOTE = {Papers from the London Mathematical Society Symposium held in
              Durham, July 9--18, 1996},
 PUBLISHER = {Cambridge University Press},
   ADDRESS = {Cambridge},
      YEAR = {1998},
     PAGES = {viii+493},
      ISBN = {0-521-64419-4},
   MRCLASS = {11-06},
  MRNUMBER = {2000a:11005},
}

@article {fontaine:groupes,
    AUTHOR = {Fontaine, J-M.},
     TITLE = {Groupes finis commutatifs sur les vecteurs de {W}itt},
   JOURNAL = {C. R. Acad. Sci. Paris S\'er. A-B},
    VOLUME = {280},
      YEAR = {1975},
     PAGES = {Ai, A1423--A1425},
   MRCLASS = {14L05},
  MRNUMBER = {51 \#10353},
MRREVIEWER = {Robert A. Morris},
}

@article {ribet:endo,
    AUTHOR = {Ribet, K.\thinspace{}A.},
     TITLE = {Endomorphisms of semi-stable abelian varieties over number
              fields},
   JOURNAL = {Ann. Math. (2)},
    VOLUME = {101},
      YEAR = {1975},
     PAGES = {555--562},
   MRCLASS = {14K15 (10D05)},
  MRNUMBER = {51 \#8120},
MRREVIEWER = {M. Kuga},
}

@article{gordon-ono:vis,
    TITLE = {Modular form {C}ongruences and {S}elmer groups},
    AUTHOR = {McGraw, W.\thinspace{}J. and Ono, K.},
    JOURNAL = {preprint},
    YEAR = {2002}
}

@book {MR2000m:11002,
    AUTHOR = {Coates, J. and Greenberg, R. and Ribet, K. A. and Rubin, K.},
     TITLE = {Arithmetic theory of elliptic curves},
      NOTE = {Lectures from the 3rd C.I.M.E.\ Session held in Cetraro, July
              12--19, 1997,
              Edited by C. Viola},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1999},
     PAGES = {viii+234},
      ISBN = {3-540-66546-3},
   MRCLASS = {11-06 (11G05)},
  MRNUMBER = {2000m:11002},
}

@incollection {ribet:torsion,
    AUTHOR = {Ribet, K.\thinspace{}A.},
     TITLE = {Torsion points on ${J}\sb 0({N})$ and {G}alois
              representations},
 BOOKTITLE = {Arithmetic theory of elliptic curves (Cetraro, 1997)},
     PAGES = {145--166},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {1999},
   MRCLASS = {11G18 (11F80)},
  MRNUMBER = {2001b:11054},
MRREVIEWER = {Matthew H. Baker},
} 


@article {merel-stein,
    AUTHOR = {Merel, L. and Stein, W.\thinspace{}A.},
     TITLE = {The field generated by the points of small prime order on an
              elliptic curve},
   JOURNAL = {Internat. Math. Res. Notices},
  FJOURNAL = {International Mathematics Research Notices},
      YEAR = {2001},
    NUMBER = {20},
     PAGES = {1075--1082},
      ISSN = {1073-7928},
   MRCLASS = {11G05},
  MRNUMBER = {1 857 596},
}

@article {hardy_littlewood:conjf,
    AUTHOR = {Hardy, G.\thinspace{}H. and Littlewood, J.\thinspace{}E.},
     TITLE = {Some {P}roblems of `{P}artitio {N}umerorum.' {I}{I}{I}. 
              {O}n the {E}xpression of a {N}umber as a {S}um of {P}rimes.},
   JOURNAL = {Acta. Math.},
    VOLUME = {44},
      YEAR = {1922},
     PAGES = {1--70}
}

@article {setzer,
    AUTHOR = {Setzer, B.},
     TITLE = {Elliptic curves of prime conductor},
   JOURNAL = {J. London Math. Soc. (2)},
    VOLUME = {10},
      YEAR = {1975},
     PAGES = {367--378},
   MRCLASS = {14K15 (10D05 14G25)},
  MRNUMBER = {51 \#8121},
MRREVIEWER = {M. Basmakov},
}

@article {neumann2,
    AUTHOR = {Neumann, O.},
     TITLE = {Elliptische {K}urven mit vorgeschriebenem
              {R}eduktionsverhalten. {I}{I}},
   JOURNAL = {Math. Nachr.},
    VOLUME = {56},
      YEAR = {1973},
     PAGES = {269--280},
   MRCLASS = {14K15 (14G25)},
  MRNUMBER = {49 \#2767b},
MRREVIEWER = {J. W. S. Cassels},
}
@article {neumann1,
    AUTHOR = {Neumann, O.},
     TITLE = {Elliptische {K}urven mit vorgeschriebenem
              {R}eduktionsverhalten. {I}},
   JOURNAL = {Math. Nachr.},
    VOLUME = {49},
      YEAR = {1971},
     PAGES = {107--123},
   MRCLASS = {14K15 (14G25)},
  MRNUMBER = {49 \#2767a},
MRREVIEWER = {J. W. S. Cassels},
}

@article {stein-watkins:ants5,
    AUTHOR = {Stein, W.\thinspace{}A. and Watkins, M.},
     TITLE = {A {D}atabase of {E}lliptic {C}urves---{F}irst {R}eport},
   JOURNAL = {Proceedings of the 5th International Symposium (ANTS-V)},
  publisher={Springer},
   address ={Berlin},
      YEAR = {2002}
}


@incollection {kolyvagin:euler_systems,
    AUTHOR = {Kolyvagin, V. A.},
     TITLE = {Euler systems},
 BOOKTITLE = {The Grothendieck Festschrift, Vol.\ II},
     PAGES = {435--483},
 PUBLISHER = {Birkh\"auser Boston},
   ADDRESS = {Boston, MA},
      YEAR = {1990},
   MRCLASS = {11R34 (11G05 11G40 11R29)},
  MRNUMBER = {92g:11109},
MRREVIEWER = {Karl Rubin},
}

@book {MR92b:00051,
     TITLE = {The {G}rothendieck {F}estschrift. {V}ol. {I}{I}},
    EDITOR = {Cartier, P. and Illusie, L. and Katz, N. M. and Laumon, G. and
              Ribet, K. A.},
      NOTE = {A collection of articles written in honor of the 60th birthday
              of Alexander Grothendieck},
 PUBLISHER = {Birkh\"auser Boston Inc.},
   ADDRESS = {Boston, MA},
      YEAR = {1990},
     PAGES = {viii+563},
      ISBN = {0-8176-3428-2},
   MRCLASS = {00B30 (11-06 14-06)},
  MRNUMBER = {92b:00051},
}

@book {lenstras:nfs,
     TITLE = {The development of the number field sieve},
    EDITOR = {Lenstra, A.\thinspace{}K. and Lenstra, Jr., H.\thinspace{}W.},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1993},
     PAGES = {viii+131},
      ISBN = {3-540-57013-6},
   MRCLASS = {11Yxx (11-06 11N35 11N36 11Y05 11Y40)},
  MRNUMBER = {96m:11116},
MRREVIEWER = {Samuel S. Wagstaff, Jr.},
}

@book{cohen:course_ant,
    AUTHOR = {Cohen, H.},
     TITLE = {A course in computational algebraic number theory},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1993},
     PAGES = {xii+534},
      ISBN = {3-540-55640-0},
   MRCLASS = {11Y40 (11Rxx 68Q40)},
  MRNUMBER = {94i:11105},
MRREVIEWER = {Joe P. Buhler},
}

@book {eisenbud_harris:geometry,
    AUTHOR = {Eisenbud, D. and Harris, J.},
     TITLE = {The geometry of schemes},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {2000},
     PAGES = {x+294},
      ISBN = {0-387-98638-3; 0-387-98637-5},
   MRCLASS = {14A15 (14-01 14C05 14H50 14N05)},
  MRNUMBER = {2001d:14002},
MRREVIEWER = {Allen B. Altman},
}

@article {kolyvagin:weil,
    AUTHOR = {Kolyvagin, V. A.},
     TITLE = {The {M}ordell-{W}eil and {S}hafarevich-{T}ate groups for
              {W}eil elliptic curves},
   JOURNAL = {Izv. Akad. Nauk SSSR Ser. Mat.},
  FJOURNAL = {Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya},
    VOLUME = {52},
      YEAR = {1988},
    NUMBER = {6},
     PAGES = {1154--1180, 1327},
      ISSN = {0373-2436},
   MRCLASS = {11G05 (11D41 11G40 14G25 14K07)},
  MRNUMBER = {90f:11035},
MRREVIEWER = {Reinhard B{\"o}lling},
}

@article {kolyvagin:subclass,
    AUTHOR = {Kolyvagin, V. A.},
     TITLE = {Finiteness of ${E}({\bf {Q}})$ and {S}{H}$({E},{\bf {Q}})$ for
              a subclass of {W}eil curves},
   JOURNAL = {Izv. Akad. Nauk SSSR Ser. Mat.},
  FJOURNAL = {Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya},
    VOLUME = {52},
      YEAR = {1988},
    NUMBER = {3},
     PAGES = {522--540, 670--671},
      ISSN = {0373-2436},
   MRCLASS = {11G05 (11G40 14G25 14K07)},
  MRNUMBER = {89m:11056},
MRREVIEWER = {Reinhard B{\"o}lling},
}


@article {edixhoven:tame,
    AUTHOR = {Edixhoven, Bas},
     TITLE = {N\'eron models and tame ramification},
   JOURNAL = {Compositio Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {81},
      YEAR = {1992},
    NUMBER = {3},
     PAGES = {291--306},
      ISSN = {0010-437X},
     CODEN = {CMPMAF},
   MRCLASS = {14K15 (11G10)},
  MRNUMBER = {93a:14041},
MRREVIEWER = {Min Ho Lee},
}

@book {guy:unsolved,
    AUTHOR = {Guy, R.\thinspace{}K.},
     TITLE = {Unsolved problems in number theory},
   EDITION = {Second},
      NOTE = {Unsolved Problems in Intuitive Mathematics, I},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {1994},
     PAGES = {xvi+285},
      ISBN = {0-387-94289-0},
   MRCLASS = {11-01 (00A07 11-02)},
  MRNUMBER = {96e:11002},
MRREVIEWER = {B. M. M. de Weger},
}

@article {lenstra-oort:additive,
    AUTHOR = {Lenstra, Jr., H. W. and Oort, F.},
     TITLE = {Abelian varieties having purely additive reduction},
   JOURNAL = {J. Pure Appl. Algebra},
  FJOURNAL = {Journal of Pure and Applied Algebra},
    VOLUME = {36},
      YEAR = {1985},
    NUMBER = {3},
     PAGES = {281--298},
      ISSN = {0022-4049},
     CODEN = {JPAAA2},
   MRCLASS = {14K15 (11G10 14G20)},
  MRNUMBER = {86e:14020},
MRREVIEWER = {Joseph H. Silverman},
}

@article {mazurtate:13,
    AUTHOR = {Mazur, B. and Tate, J.},
     TITLE = {Points of order $13$ on elliptic curves},
   JOURNAL = {Invent. Math.},
    VOLUME = {22},
      YEAR = {1973/74},
     PAGES = {41--49},
   MRCLASS = {14G05 (14H40 14K15)},
  MRNUMBER = {50 \#327},
MRREVIEWER = {F. Oort},
}

@incollection {ogg:rational13,
    AUTHOR = {Ogg, A. P.},
     TITLE = {Rational points on certain elliptic modular curves},
 BOOKTITLE = {Analytic number theory (Proc. Sympos. Pure Math., Vol XXIV,
              St. Louis Univ., St. Louis, Mo., 1972)},
     PAGES = {221--231},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, R.I.},
      YEAR = {1973},
   MRCLASS = {14G05 (10D05 14K15)},
  MRNUMBER = {49 \#2743},
MRREVIEWER = {J. W. S. Cassels},
}

@article{watanabe:reflections,
    AUTHOR = {Watanabe, J.},
     TITLE = {Some remarks on {C}ohen-{M}acaulay rings with many zero
              divisors and an application},
   JOURNAL = {J. Algebra},
    VOLUME = {39},
      YEAR = {1976},
    NUMBER = {1},
     PAGES = {1--14},
   MRCLASS = {14M15 (13H10)},
  MRNUMBER = {53 \#2968},
MRREVIEWER = {Jean-Luc Chabert},
}

@article {chevalley:thm,
    AUTHOR = {Chevalley, C.},
     TITLE = {Une d\'emonstration d'un th\'eor\`eme sur les groupes
              alg\'ebriques},
   JOURNAL = {J. Math. Pures Appl. (9)},
    VOLUME = {39},
      YEAR = {1960},
     PAGES = {307--317},
   MRCLASS = {14.50},
  MRNUMBER = {23 \#A3743},
MRREVIEWER = {I. Barsotti},
}



@article {cassels:arithmeticIII,
    AUTHOR = {Cassels, J.\thinspace{}W.\thinspace{}S.},
     TITLE = {Corrigendum: ``{A}rithmetic on curves of genus $1$. {I}{I}{I}.
              {T}he {T}ate-\v {S}afarevi\v c and {S}elmer groups''},
   JOURNAL = {Proc. London Math. Soc. (3)},
    VOLUME = {13},
      YEAR = {1963},
     PAGES = {768},
   MRCLASS = {14.49},
  MRNUMBER = {29 \#1213},
}

@incollection {tate:duality,
    AUTHOR = {Tate, J.},
     TITLE = {Duality theorems in {G}alois cohomology over number fields},
 BOOKTITLE = {Proc. Internat. Congr. Mathematicians (Stockholm, 1962)},
     PAGES = {288--295},
 PUBLISHER = {Inst. Mittag-Leffler},
   ADDRESS = {Djursholm},
      YEAR = {1963},
   MRCLASS = {10.66},
  MRNUMBER = {31 \#168},
}

@article{mazur:visthree,
    AUTHOR = {Mazur, B.},
     TITLE = {Visualizing elements of order three in the
              {S}hafarevich-{T}ate group},
   JOURNAL = {Asian J. Math.},
  FJOURNAL = {The Asian Journal of Mathematics},
    VOLUME = {3},
      YEAR = {1999},
    NUMBER = {1},
     PAGES = {221--232},
      ISSN = {1093-6106},
   MRCLASS = {11G05 (14G05)},
  MRNUMBER = {2000g:11048},
MRREVIEWER = {Odile Sauzet},
}

@article{emerton:optimal,
   author = {Emerton, M.},
   title  = {Optimal {Q}uotients of {M}odular {J}acobians},
   journal = {preprint},
   year = {2001}
}


@article{buzzard-taylor,
   AUTHOR = {Buzzard, K. and Taylor, R.},
    TITLE = {Companion forms and weight one forms},
  JOURNAL = {Ann. of Math. (2)},
 FJOURNAL = {Annals of Mathematics. Second Series},
   VOLUME = {149},
     YEAR = {1999},
   NUMBER = {3},
    PAGES = {905--919},
     ISSN = {0003-486X},
    CODEN = {ANMAAH},
  MRCLASS = {11Fxx},
 MRNUMBER = {1 709 306},
}


@proceedings {MR98g:11001,
    TITLE = {Computational perspectives on number theory},
BOOKTITLE = {Proceedings of the conference in honor of A. O. L. Atkin held
             at the University of Illinois, Chicago, IL, September 1995},
   EDITOR = {Buell, D. A. and Teitelbaum, J. T.},
PUBLISHER = {American Mathematical Society},
  ADDRESS = {Providence, RI},
     YEAR = {1998},
    PAGES = {x+232},
     ISBN = {0-8218-0880-X},
  MRCLASS = {11-01 (00B30 11Yxx)},
 MRNUMBER = {98g:11001},
}

@incollection {birch:atkin,
   AUTHOR = {Birch, B.},
    TITLE = {Atkin and the {A}tlas {L}ab},
BOOKTITLE = {Proceedings of the conference in honor of 
             A.\thinspace{}O.\thinspace{}L. Atkin held
             at the University of Illinois, Chicago, IL, September 1995},
    PAGES = {13--20},
PUBLISHER = {Amer. Math. Soc.},
  ADDRESS = {Providence, RI},
     YEAR = {1998},
  MRCLASS = {11-03 (01A60 11F30 11F33)},
 MRNUMBER = {99c:11002},
   MRREVR = {V. Kumar Murty},
}


@proceedings {MR50:16,
    TITLE = {S\'eminaire Bourbaki},
BOOKTITLE = {S\'eminaire Bourbaki, 24\`eme ann\'ee (1971/1972), Exp. No.
             414},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {1973},
    PAGES = {iv+361},
  MRCLASS = {00A10},
 MRNUMBER = {50 #16},
}

@incollection{mazur:symboles,
   AUTHOR = {Mazur, B.},
    TITLE = {Courbes elliptiques et symboles modulaires},
BOOKTITLE = {S\'eminaire Bourbaki, 24\`eme ann\'ee (1971/1972), Exp. No.
             414},
    PAGES = {277--294. Lecture Notes in Math., Vol. 317},
PUBLISHER = {Springer},
  ADDRESS = {Berlin},
     YEAR = {1973},
  MRCLASS = {14K15 (14G25 10D15)},
 MRNUMBER = {55 #2930},
   MRREVR = {Jacques Velu},
}



@article {mazur:arithmetic_values,
   AUTHOR = {Mazur, B.},
    TITLE = {On the arithmetic of special values of ${L}$\ functions},
  JOURNAL = {Invent. Math.},
 FJOURNAL = {Inventiones Mathematicae},
   VOLUME = {55},
     YEAR = {1979},
   NUMBER = {3},
    PAGES = {207--240},
     ISSN = {0020-9910},
    CODEN = {INVMBH},
  MRCLASS = {14G10 (10D24 12A70 14G25 14K07)},
 MRNUMBER = {82e:14033},
   MRREVR = {V. V. Shokurov},
}



@article {hatada:eigenvalues79,
    AUTHOR = {Hatada, K.},
     TITLE = {Eigenvalues of {H}ecke operators on 
\protect{${\rm {S}{L}}(2,\,{\bf {Z}})$}},
   JOURNAL = {Math. Ann.},
  FJOURNAL = {Mathematische Annalen},
    VOLUME = {239},
      YEAR = {1979},
    NUMBER = {1},
     PAGES = {75--96},
      ISSN = {0025-5831},
     CODEN = {MAANA3},
   MRCLASS = {10D15},
  MRNUMBER = {80b:10037},
MRREVIEWER = {Roy Fuller},
}

@article {hatada:rationality,
   AUTHOR = {Hatada, K.},
    TITLE = {Multiplicity one theorem and modular symbols},
  JOURNAL = {J. Math. Soc. Japan},
 FJOURNAL = {Journal of the Mathematical Society of Japan},
   VOLUME = {33},
     YEAR = {1981},
   NUMBER = {3},
    PAGES = {445--470},
     ISSN = {0025-5645},
    CODEN = {NISUBC},
  MRCLASS = {10D12 (12A65)},
 MRNUMBER = {83d:10030},
   MRREVR = {Wen Ch'ing Winnie Li},
}


@article {sokurov:modsym,
   AUTHOR = {{\v{S}}okurov, V. V.},
    TITLE = {Modular symbols of arbitrary weight},
  JOURNAL = {Funkcional. Anal. i Prilo\v zen.},
   VOLUME = {10},
     YEAR = {1976},
   NUMBER = {1},
    PAGES = {95--96},
  MRCLASS = {10D05},
 MRNUMBER = {55 #269},
   MRREVR = {K.-B. Gundlach},
}

@article {goldfeld:complexity,
   AUTHOR = {Goldfeld, D.},
    TITLE = {On the computational complexity of modular symbols},
  JOURNAL = {Math. Comp.},
 FJOURNAL = {Mathematics of Computation},
   VOLUME = {58},
     YEAR = {1992},
   NUMBER = {198},
    PAGES = {807--814},
     ISSN = {0025-5718},
    CODEN = {MCMPAF},
  MRCLASS = {11F67 (11Y35)},
 MRNUMBER = {93a:11042},
   MRREVR = {Glenn Stevens},
}


@article{ganz-lario:manin,
   AUTHOR = {Gonz\'{a}lez, J. and Lario, J-C.},
   TITLE = {$\mathbf{Q}$-curves and their {M}anin ideals},
   JOURNAL = {preprint}, 
    YEAR = {2000}
}

@article {mazur-sd,
   AUTHOR = {Mazur, B. and Swinnerton-Dyer, P.},
    TITLE = {Arithmetic of {W}eil curves},
  JOURNAL = {Invent. Math.},
   VOLUME = {25},
     YEAR = {1974},
    PAGES = {1--61},
  MRCLASS = {14G05 (10D05)},
 MRNUMBER = {50 #7152},
   MRREVR = {J. S. Milne},
}


@article {darmon-merel,
   AUTHOR = {Darmon, H. and Merel, L.},
    TITLE = {Winding quotients and some variants of {F}ermat's last theorem},
  JOURNAL = {J. Reine Angew. Math.},
 FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik},
   VOLUME = {490},
     YEAR = {1997},
    PAGES = {81--100},
     ISSN = {0075-4102},
    CODEN = {JRMAA8},
  MRCLASS = {11G18 (11D41 11F80 11G05)},
 MRNUMBER = {98h:11076},
   MRREVR = {Kenneth Kramer},
}


@proceedings {motives,
    TITLE = {Motives},
BOOKTITLE = {Proceedings of the AMS-IMS-SIAM Joint Summer Research
             Conference held at the University of Washington, Seattle,
             Washington, July 20--August 2, 1991},
   EDITOR = {Jannsen, Uwe and Kleiman, Steven and Serre, Jean-Pierre},
PUBLISHER = {American Mathematical Society},
  ADDRESS = {Providence, RI},
     YEAR = {1994},
    PAGES = {xiv+747},
     ISBN = {0-8218-1636-5},
  MRCLASS = {11-06 (19-06)},
 MRNUMBER = {94i:11003},
}

@incollection {gross:central,
   AUTHOR = {Gross, B.\thinspace{}H.},
    TITLE = {${L}$-functions at the central critical point},
BOOKTITLE = {Motives (Seattle, WA, 1991)},
    PAGES = {527--535},
PUBLISHER = {Amer. Math. Soc.},
  ADDRESS = {Providence, RI},
     YEAR = {1994},
  MRCLASS = {11G40 (14G10)},
 MRNUMBER = {95a:11060},
   MRREVR = {Jan Nekov{\'a}{\v{r}}},
}

@book {stevens:thesis,
   AUTHOR = {Stevens, G.},
    TITLE = {Arithmetic on modular curves},
PUBLISHER = {Birkh\"auser Boston Inc.},
  ADDRESS = {Boston, Mass.},
     YEAR = {1982},
    PAGES = {xvii+214},
     ISBN = {3-7643-3088-0},
  MRCLASS = {11G40 (11F67 11G30 14G10 14G13)},
 MRNUMBER = {87b:11050},
   MRREVR = {Ernst Kani},
}

@book {hellegouarch:invitation,
   AUTHOR = {Hellegouarch, Y.},
    TITLE = {Invitation aux math\'ematiques de {F}ermat-{W}iles},
PUBLISHER = {Masson},
  ADDRESS = {Paris},
     YEAR = {1997},
    PAGES = {viii+401},
     ISBN = {2-225-83008-8},
  MRCLASS = {11-01 (11D41 11F11 11G05 11G18)},
 MRNUMBER = {99e:11001},
   MRREVR = {Massimo Bertolini},
}

@book{cime-1997,
author="Viola, C.",
title="{Arithmetic theory of elliptic curves. Lectures given at the 3rd session of the {C}entro {I}nternazionale {M}atematico {E}stivo \protect{(CIME)}.}",
language="English",
source="{{L}ecture {N}otes in {M}athematics. 1716. {B}erlin: {S}pringer. viii, 260 p. DM 74.00; oeS 541.00; sFr. 67.50; \sterling 28.50; \$ 52.80 (1999). [ISBN 3-540-66546-3/hbk; ISSN 0075-8434]}",
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {1997},
    PAGES = {260}
}

@incollection {darmon-bsd,
   AUTHOR = {Darmon, H.},
    TITLE = {Wiles' theorem and the arithmetic of elliptic curves},
BOOKTITLE = {Modular forms and Fermat's last theorem (Boston, MA, 1995)},
    PAGES = {549--569},
PUBLISHER = {Springer},
  ADDRESS = {New York},
     YEAR = {1997},
  MRCLASS = {11G40 (11G05)},
 MRNUMBER = {1 638 495},
}

@article {joshi,
   AUTHOR = {Joshi, Kirti},
    TITLE = {Remarks on methods of {F}ontaine and {F}altings},
  JOURNAL = {Internat. Math. Res. Notices},
 FJOURNAL = {International Mathematics Research Notices},
   VOLUME = {1999},
   NUMBER = {22},
    PAGES = {1199--1209},
     ISSN = {1073-7928},
  MRCLASS = {11Fxx},
 MRNUMBER = {1 731 472},
}

@incollection {serre:cnrs,
   AUTHOR = {Serre, Jean-Pierre},
    TITLE = {Groupes de {L}ie $l$-adiques attach\'es aux courbes
             elliptiques},
BOOKTITLE = {Les Tendances G\'eom. en Alg\'ebre et Th\'eorie des Nombres},
    PAGES = {239--256},
PUBLISHER = {\'Editions du Centre National de la Recherche Scientifique,
             Paris},
     YEAR = {1966},
  MRCLASS = {14.50},
 MRNUMBER = {36 #1453},
   MRREVR = {H. Popp},
}

@article {ramakrishna:lift2,
   AUTHOR = {Ramakrishna, R.},
    TITLE = {Deforming {G}alois representations and the conjectures
             of {S}erre and {F}ontaine-{M}azur},
  JOURNAL = {preprint, 
             \protect{\sf ftp://math.cornell.edu/pub/ravi}},
 FJOURNAL = {},
   VOLUME = {},
     YEAR = {2000},
   NUMBER = {},
    PAGES = {},
}

@article {ramakrishna:lifting,
   AUTHOR = {Ramakrishna, R.},
    TITLE = {Lifting {G}alois representations},
  JOURNAL = {Invent. Math.},
 FJOURNAL = {Inventiones Mathematicae},
   VOLUME = {138},
     YEAR = {1999},
   NUMBER = {3},
    PAGES = {537--562},
     ISSN = {0020-9910},
    CODEN = {INVMBH},
  MRCLASS = {11Fxx},
 MRNUMBER = {1 719 819},
}

@article {ramakrishna:deform,
   AUTHOR = {Ramakrishna, R.},
    TITLE = {Deforming an even representation},
  JOURNAL = {Invent. Math.},
 FJOURNAL = {Inventiones Mathematicae},
   VOLUME = {132},
     YEAR = {1998},
   NUMBER = {3},
    PAGES = {563--580},
     ISSN = {0020-9910},
    CODEN = {INVMBH},
  MRCLASS = {11R32 (11R34)},
 MRNUMBER = {99h:11128},
   MRREVR = {Nigel Boston},
}


@book {haberland,
   AUTHOR = {Haberland, Klaus},
    TITLE = {Galois cohomology of algebraic number fields},
     NOTE = {With two appendices by Helmut Koch and Thomas Zink},
PUBLISHER = {VEB Deutscher Verlag der Wissenschaften},
  ADDRESS = {Berlin},
     YEAR = {1978},
    PAGES = {145},
  MRCLASS = {12A60},
 MRNUMBER = {81i:12009},
   MRREVR = {Chih-Han Sah},
}



@article{dummigan:cp,
   author = {Dummigan, N.},
   title  = {Period ratios of modular forms},
   journal= {to appear in Math. Annalen}
}


@article {cohen-oesterle:dimensions,
   AUTHOR = {Cohen, H. and Oesterl{\'e}, J.},
    TITLE = {Dimensions des espaces de formes modulaires},
BOOKTITLE = {Modular functions of one variable, VI (Proc. Second Internat.
             Conf., Univ. Bonn, Bonn, 1976)},
    PAGES = {69--78. Lecture Notes in Math., Vol. 627},
PUBLISHER = {Springer},
  ADDRESS = {Berlin},
     YEAR = {1977},
  MRCLASS = {10D15},
 MRNUMBER = {57 #12396},
   MRREVR = {R. A. Rankin},
}

@book{robert:elliptic,
   AUTHOR = {Robert, A.},
    TITLE = {Elliptic curves},
     NOTE = {Notes from postgraduate lectures given in Lausanne 1971/72,
             Lecture Notes in Mathematics, Vol. 326},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {1973},
    PAGES = {viii+264},
  MRCLASS = {14K15},
 MRNUMBER = {50 #4594},
   MRREVR = {Kuang-yen Shih}
}

@book {dixcohomologie,
    TITLE = {Dix expos\'es sur la cohomologie des sch\'emas},
     NOTE = {Advanced Studies in Pure Mathematics, Vol. 3},
PUBLISHER = {North-Holland Publishing Co.},
  ADDRESS = {Amsterdam},
     YEAR = {1968},
    PAGES = {vi+386},
  MRCLASS = {14.55},
 MRNUMBER = {39 #2777},
}

@incollection {grothendieck:brauer3,
   AUTHOR = {Grothendieck, Alexander},
    TITLE = {Le groupe de {B}rauer. {I}{I}{I}. {E}xemples et compl\'ements},
BOOKTITLE = {Dix Expos\'es sur la Cohomologie des Sch\'emas},
    PAGES = {88--188},
PUBLISHER = {North-Holland},
  ADDRESS = {Amsterdam},
     YEAR = {1968},
  MRCLASS = {14.55},
 MRNUMBER = {39 #5586c},
   MRREVR = {J. S. Milne},
}
@incollection {grothendieck:brauer2,
   AUTHOR = {Grothendieck, Alexander},
    TITLE = {Le groupe de {B}rauer. {I}{I}. {T}h\'eorie cohomologique},
BOOKTITLE = {Dix Expos\'es sur la Cohomologie des Sch\'emas},
    PAGES = {67--87},
PUBLISHER = {North-Holland},
  ADDRESS = {Amsterdam},
     YEAR = {1968},
  MRCLASS = {14.55},
 MRNUMBER = {39 #5586b},
}
@incollection {grothendieck:brauer1,
   AUTHOR = {Grothendieck, Alexander},
    TITLE = {Le groupe de {B}rauer. {I}. {A}lg\`ebres d'{A}zumaya et
             interpr\'etations diverses},
BOOKTITLE = {Dix Expos\'es sur la Cohomologie des Sch\'emas},
    PAGES = {46--66},
PUBLISHER = {North-Holland},
  ADDRESS = {Amsterdam},
     YEAR = {1968},
  MRCLASS = {14.55},
 MRNUMBER = {39 #5586a},
}

@book {eisenbud-harris-2,
   AUTHOR = {Eisenbud, D. and Harris, J.},
   TITLE = {{S}chemes, {T}he language of modern algebraic geometry},
     NOTE = {Graduate Texts in Mathematics, Vol.\ 197},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {},
    PAGES = {}
}

@book {eisenbud-harris,
   AUTHOR = {Eisenbud, D. and Harris, J.},
    TITLE = {{S}chemes, {T}he language of modern algebraic geometry},
PUBLISHER = {Wadsworth \& Brooks/Cole Advanced Books \& Software},
  ADDRESS = {Pacific Grove, CA},
     YEAR = {1992},
    PAGES = {xii+157},
     ISBN = {0-534-17606-2; 0-534-17604-6},
  MRCLASS = {14-01 (14A15)},
 MRNUMBER = {93k:14001},
   MRREVR = {Alexey N. Rudakov},
}



@article {coleman:serre,
   AUTHOR = {Coleman, R.\thinspace{}F.},
    TITLE = {Serre's conjecture: {T}he {J}ugentraum of the 20th century},
     NOTE = {XII School of Algebra, Part I (Portuguese) (Diamantina, 1992)},
  JOURNAL = {Mat. Contemp.},
 FJOURNAL = {Matem\'atica Contempor\cflex anea},
   VOLUME = {6},
     YEAR = {1994},
    PAGES = {13--18},
     ISSN = {0103-9059},
  MRCLASS = {12F05 (11F03 12F12)},
 MRNUMBER = {95j:12003},
   MRREVR = {Henri Darmon},
}

@article {edixhoven:erratum,
   AUTHOR = {Edixhoven, B.},
    TITLE = {Erratum and addendum: ``{T}he role of {S}erre's conjecture in
             the proof of {F}ermat's theorem''},
  JOURNAL = {Gaz. Math.},
 FJOURNAL = {Gazette des Math\'ematiciens},
   NUMBER = {67},
     YEAR = {1996},
    PAGES = {19},
     ISSN = {0224-8999},
  MRCLASS = {11F33 (11D41 11F80 11G05)},
 MRNUMBER = {96k:11055b},
   MRREVR = {Fernando Q. Gouv\^ea},
}

@article {edixhoven:serrerole,
   AUTHOR = {Edixhoven, B.},
    TITLE = {Le r\^{o}le de la conjecture de {S}erre dans la
             d\'emonstration du th\'eor\`eme de {F}ermat},
  JOURNAL = {Gaz. Math.},
 FJOURNAL = {Gazette des Math\'ematiciens},
   NUMBER = {66},
     YEAR = {1995},
    PAGES = {25--41},
     ISSN = {0224-8999},
  MRCLASS = {11F33 (11D41 11F80 11G05)},
 MRNUMBER = {96k:11055a},
   MRREVR = {Fernando Q. Gouv\^ea},
}


@article {gouvea-mazur:families,
   AUTHOR = {Gouv\^ea, F. and Mazur, B.},
    TITLE = {Families of modular eigenforms},
  JOURNAL = {Math. Comp.},
 FJOURNAL = {Mathematics of Computation},
   VOLUME = {58},
     YEAR = {1992},
   NUMBER = {198},
    PAGES = {793--805},
     ISSN = {0025-5718},
    CODEN = {MCMPAF},
  MRCLASS = {11F33 (11Y35 14G20)},
 MRNUMBER = {93d:11049},
   MRREVR = {Bas Edixhoven},
}

@incollection {eigencurve,
   AUTHOR = {Coleman, R. and Mazur, B.},
    TITLE = {The {E}igencurve},
BOOKTITLE = {Galois representations in arithmetic algebraic geometry
             (Durham, 1996)},
    PAGES = {1--113},
PUBLISHER = {Cambridge Univ. Press},
  ADDRESS = {Cambridge},
     YEAR = {1998},
  MRCLASS = {11Fxx (11Gxx)},
 MRNUMBER = {1 696 469},
}



@book {eisenbud,
   AUTHOR = {Eisenbud, D.},
    TITLE = {Commutative Algebra with a View Toward Algebraic Geometry},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {New York},
     YEAR = {1995},
    PAGES = {xvi+785},
     ISBN = {0-387-94268-8; 0-387-94269-6},
  MRCLASS = {13-01 (14A05)},
 MRNUMBER = {97a:13001},
   MRREVR = {Matthew Miller},
}

@book {cassels-flynn,
   AUTHOR = {Cassels, J.\thinspace{}W.\thinspace{}S. 
            and Flynn, E.\thinspace{}V.},
    TITLE = {Prolegomena to a middlebrow arithmetic of curves 
             of genus \protect{$2$}},
PUBLISHER = {Cambridge University Press},
  ADDRESS = {Cambridge},
     YEAR = {1996},
    PAGES = {xiv+219},
     ISBN = {0-521-48370-0},
  MRCLASS = {11G30 (11Y50 14G25)},
 MRNUMBER = {97i:11071},
   MRREVR = {Joseph H. Silverman},
}

@book {neronmodels,
   AUTHOR = {Bosch, S. and L{\"u}tkebohmert, W. and Raynaud, M.},
    TITLE = {N\'eron models},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {1990},
    PAGES = {x+325},
     ISBN = {3-540-50587-3},
  MRCLASS = {14K15 (11G10 14L15)},
 MRNUMBER = {91i:14034},
   MRREVR = {J. Milne},
}


@article {hida:iwasawa,
   AUTHOR = {Hida, H.},
    TITLE = {Iwasawa modules attached to congruences of cusp forms},
  JOURNAL = {Ann. Sci. \'Ecole Norm. Sup. (4)},
 FJOURNAL = {Annales Scientifiques de l'\'Ecole Normale Sup\'erieure.
             Quatri\`eme S\'erie},
   VOLUME = {19},
     YEAR = {1986},
   NUMBER = {2},
    PAGES = {231--273},
     ISSN = {0012-9593},
    CODEN = {ASENAH},
  MRCLASS = {11F33 (11G18 11R23)},
 MRNUMBER = {88i:11023},
   MRREVR = {Yasutaka Ihara},
}



@article {hida:invent86,
   AUTHOR = {Hida, H.},
    TITLE = {Galois representations into 
             \protect{${\rm {G}{L}}\sb 2({\bf {Z}}\sb
             p[[{X}]])$} attached to ordinary cusp forms},
  JOURNAL = {Invent. Math.},
 FJOURNAL = {Inventiones Mathematicae},
   VOLUME = {85},
     YEAR = {1986},
   NUMBER = {3},
    PAGES = {545--613},
     ISSN = {0020-9910},
    CODEN = {INVMBH},
  MRCLASS = {11F11 (11F33 11F85 11R23)},
 MRNUMBER = {87k:11049},
   MRREVR = {Ernst-Wilhelm Zink},
}


@incollection {elkies:heegner,
   AUTHOR = {Elkies, N.\thinspace{}D.},
    TITLE = {Heegner point computations},
BOOKTITLE = {Algorithmic number theory (Ithaca, NY, 1994)},
    PAGES = {122--133},
PUBLISHER = {Springer},
  ADDRESS = {Berlin},
     YEAR = {1994},
}
@article {scholl:motivesinvent,
   AUTHOR = {Scholl, A.\thinspace{}J.},
    TITLE = {Motives for modular forms},
  JOURNAL = {Invent. Math.},
 FJOURNAL = {Inventiones Mathematicae},
   VOLUME = {100},
     YEAR = {1990},
   NUMBER = {2},
    PAGES = {419--430},
     ISSN = {0020-9910},
    CODEN = {INVMBH},
}
@incollection {scholl:kato,
   author = {Scholl, A.\thinspace{}J.},
   title  = {An introduction to {K}ato's {E}uler systems},
  booktitle = {Galois Representations in Arithmetic Algebraic Geometry},
    pages = {379--460},
   year   = {1998},
  publisher = {Cambridge University Press}
}

@proceedings {lms254,
   title  = {Galois Representations in Arithmetic Algebraic Geometry},
  booktitle = {Galois Representations in Arithmetic Algebraic Geometry},
   editor = {Scholl A.\thinspace{}J. and Taylor R.\thinspace{}L.},
   pages  = {493},
   year   = {1998},
  publisher = {Cambridge University Press}
}

%qa1.h3
@article{artin:conjecture,
   author = {Artin, E.},
   title  = {{\"U}ber eine neue {A}rt von {L}-Reihen},
   journal={Abh. Math. Sem. Univ. Hamburg},
   volume ={3},
   year   ={1923 or 1924??? CHECK!},
   pages  ={89--108}
}   

@article{artin:conjecture2,
   author = {Artin, E},
   title  = {Zur {T}heorie der {L}-{R}eihen mit allgemeinen 
             {G}ruppencharakteren},
   journal={Abh. math. Semin. Univ. Hamburg},
   volume ={8},
   year   ={1930},
   pages  ={292--306}
}   

@article{buzzard-stein:artin,
   AUTHOR = {Buzzard, K. and Stein, W.\thinspace{}A.},
   title  = {Modularity of some icosahedral {G}alois representations},
  journal = {in preparation}
}

@proceedings {MR98g:11001,
    TITLE = {Computational perspectives on number theory},
BOOKTITLE = {Proceedings of the conference in honor of A. O. L. Atkin held
             at the University of Illinois, Chicago, IL, September 1995},
   EDITOR = {Buell, D. A. and Teitelbaum, J. T.},
PUBLISHER = {American Mathematical Society},
  ADDRESS = {Providence, RI},
     YEAR = {1998},
    PAGES = {x+232},
     ISBN = {0-8218-0880-X},
}


@proceedings {MR95j:11119,
    TITLE = {Algorithmic number theory},
BOOKTITLE = {Proceedings of the First International Symposium (ANTS-I) held
             at Cornell University, Ithaca, New York, May 6--9, 1994},
   EDITOR = {Adleman, Leonard M. and Huang, Ming-Deh},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {1994},
    PAGES = {x+323},
     ISBN = {3-540-58691-1},
}



@incollection {elkies:ffield,
   AUTHOR = {Elkies, N.\thinspace{}D.},
    TITLE = {Elliptic and modular curves over finite fields and related
             computational issues},
BOOKTITLE = {Computational perspectives on number theory (Chicago, IL,
             1995)},
    PAGES = {21--76},
PUBLISHER = {Amer. Math. Soc.},
  ADDRESS = {Providence, RI},
     YEAR = {1998},
}



@article {jones:thesis,
   author = {Jones, D.\thinspace{}M.},
   title = {On modular {G}alois representations in characteristic $3$},
   year  = {1998},
   journal = {U.\thinspace{}C. Berkeley Ph.D. thesis}
}

@article {agashe-stein:manin,
   AUTHOR = {Agashe, A. and Stein, W.\thinspace{}A.},
    TITLE = {The generalized {M}anin constant, congruence primes,
and the modular degree},
     YEAR = {2002},
  journal = {In preparation}
}

@article {stein:vismordell,
   AUTHOR = {Stein, W.\thinspace{}A.},
    TITLE = {{V}isualizing {M}ordell-{W}eil {G}roups of {E}lliptic {C}urves {U}sing
             {S}hafarevich-{T}ate {G}roups},
     YEAR = {2002},
  journal = {In preparation}
}


@article {ash-stevens,
   AUTHOR = {Ash, A. and Stevens, G.},
    TITLE = {Cohomology of arithmetic groups and congruences between systems
             of {H}ecke eigenvalues},
  JOURNAL = {J. Reine Angew. Math.},
 FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik},
   VOLUME = {365},
     YEAR = {1986},
    PAGES = {192--220},
     ISSN = {0075-4102},
    CODEN = {JRMAA8},
}

@article {buzzard:level,
  author = {Buzzard, K.},
  title  = {On level-lowering for mod 2 representations},
  journal= {preprint}
}


@article {RAMA,
  author  = {Ramakrishna, R.},
   title  = {Lifting {G}alois representations},
 journal  = {preprint}
}

@article {SBTAYLOR,
   AUTHOR = {Shepherd-Barron, N. I. and Taylor, R.},
    TITLE = {Mod 2 and mod 5 icosahedral representations},
  JOURNAL = {J. Amer. Math. Soc.},
 FJOURNAL = {Journal of the American Mathematical Society},
   VOLUME = {10},
     YEAR = {1997},
   NUMBER = {2},
    PAGES = {283--298},
     ISSN = {0894-0347},
}

@article {DOUD,
   AUTHOR = {Doud, D.},
    TITLE = {\protect{${S}\sb 4$} and \protect{$\tilde {S}{}\sb 4$} 
              extensions of \protect{${\bf {Q}}$}
             ramified at only one prime},
  JOURNAL = {J. Number Theory},
 FJOURNAL = {Journal of Number Theory},
   VOLUME = {75},
     YEAR = {1999},
   NUMBER = {2},
    PAGES = {185--197},
     ISSN = {0022-314X},
    CODEN = {JNUTA9},
}


@proceedings {MR90b:11003,
    TITLE = {Number theory},
BOOKTITLE = {Proceedings of the Fifteenth Journ\'ees Arithm\'etiques held at
             the University of Ulm, Ulm, September 14--18, 1987},
   EDITOR = {Schlickewei, H. P. and Wirsing, E.},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {New York},
     YEAR = {1989},
    PAGES = {vi+266},
     ISBN = {0-387-51397-3},
}

@incollection {FREYTWO,
   AUTHOR = {Frey, G.},
    TITLE = {Links between solutions of 
                  \protect{${A}-{B}={C}$} and elliptic curves},
BOOKTITLE = {Number theory (Ulm, 1987)},
    PAGES = {31--62},
PUBLISHER = {Springer},
  ADDRESS = {New York},
     YEAR = {1989},
}
@article {FREYONE,
   AUTHOR = {Frey, G.},
    TITLE = {Links between stable elliptic curves and 
              certain {D}iophantine \protect{\nobreak{equations}}},
  JOURNAL = {Ann. Univ. Sarav. Ser. Math.},
 FJOURNAL = {Annales Universitatis Saraviensis. Series Mathematicae},
   VOLUME = {1},
     YEAR = {1986},
   NUMBER = {1},
    PAGES = {iv+40},
}


@article {fujiwara,
   author = {Fujiwara, K.},
   title  = {Level optimization in the totally real case},
   journal= {in preparation},
   year   = {1999}
}

@article {jarvis:mazur,
   AUTHOR = {Jarvis, F.},
    TITLE = {Mazur's principle for totally real fields of odd degree},
  JOURNAL = {Compositio Math.},
 FJOURNAL = {Compositio Mathematica},
   VOLUME = {116},
     YEAR = {1999},
   NUMBER = {1},
    PAGES = {39--79},
     ISSN = {0010-437X},
    CODEN = {CMPMAF},
}
@article {jarvis:level,
   AUTHOR = {Jarvis, F.},
    TITLE = {Level lowering for modular mod \protect{$\ell$} 
             representations over totally real fields\-},
  JOURNAL = {Math. Ann.},
 FJOURNAL = {Mathematische Annalen},
   VOLUME = {313},
     YEAR = {1999},
   NUMBER = {1},
    PAGES = {141--160},
     ISSN = {0025-5831},
    CODEN = {MAANA},
}
@article {jarvis:hilbert,
   AUTHOR = {Jarvis, F.},
    TITLE = {On \protect{G}alois representations     
            associated to \protect{H}ilbert modular
             forms},
  JOURNAL = {J. Reine Angew. Math.},
 FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik},
   VOLUME = {491},
     YEAR = {1997},
    PAGES = {199--216},
     ISSN = {0075-4102},
    CODEN = {JRMAA8},
}

@inproceedings {JPS,
   AUTHOR = {Serre, J-P.},
    TITLE = {Congruences et formes modulaires [d'apr\`es 
            {H}.\thinspace{}{P}.\thinspace{}{F}.\
             {S}winnerton-{D}yer]},
BOOKTITLE = {S\'eminaire Bourbaki, 24e ann\'ee (1971/1972), Exp. No. 416},
    PAGES = {319--338. Lecture Notes in Math., Vol. 317},
PUBLISHER = {Springer},
  ADDRESS = {Berlin},
     YEAR = {1973},
}

@book {MR50:16,
    TITLE = {S\'eminaire Bourbaki, 24e ann\'ee (1971/1972), Exp. No. 416},
     NOTE = {Vol. 1971/1972, 24e ann\'ee: Expos\'es Nos. 400--417,
             Lecture Notes in Mathematics, Vol. 317},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {1973},
    PAGES = {iv+361},
  MRCLASS = {00A10},
 MRNUMBER = {50 #16},
}

@article{agashe,
   AUTHOR = {Agashe, A.},
    TITLE = {On invisible elements of the {T}ate-{S}hafarevich group},
  JOURNAL = {C. R. Acad. Sci. Paris S\'er. I Math.},
 FJOURNAL = {Comptes Rendus de l'Acad\'emie des Sciences. S\'erie I.
             Math\'ematique},
   VOLUME = {328},
     YEAR = {1999},
   NUMBER = {5},
    PAGES = {369--374},
     ISSN = {0764-4442},
    CODEN = {CASMEI},
  MRCLASS = {11Gxx},
 MRNUMBER = {1 678 131},
}


@incollection {bloch-kato,
   AUTHOR = {Bloch, S. and Kato, K.},
    TITLE = {\protect{${L}$}-functions and 
                  \protect{T}amagawa numbers of motives},
BOOKTITLE = {The Grothendieck Festschrift, Vol. \protect{I}},
    PAGES = {333--400},
PUBLISHER = {Birkh\"auser Boston},
  ADDRESS = {Boston, MA},
     YEAR = {1990},
}

@book {MR91h:00035,
    TITLE = {The \protect{G}rothendieck 
              \protect{F}estschrift. \protect{V}ol. \protect{I}},
   EDITOR = {Cartier, P. and Illusie, L. and Katz, N.\thinspace{}M. 
             and Laumon, G. and Manin, Yu. and Ribet, K.\thinspace{}A.},
     NOTE = {A collection of articles written in honor of the 60th birthday
             of Alexander Grothendieck},
PUBLISHER = {Birkh\"auser Boston Inc.},
  ADDRESS = {Boston, MA},
     YEAR = {1990},
    PAGES = {xx+498},
     ISBN = {0-8176-3427-4},
}

@book {antwerpiv,
    TITLE = {Modular functions of one variable. {I}{V}},
BOOKTITLE = {Proceedings of the International Summer School on Modular
             Functions of One Variable and Arithmetical Applications, RUCA,
             University of Antwerp, Antwerp, July 17--August 3, 1972},
   EDITOR = {Birch, B.\thinspace{}J. and Kuyk, W.},
     NOTE = {Lecture Notes in Mathematics, Vol. 476},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {1975},
    PAGES = {iv+151},
}

@incollection{birch:bsd,
   AUTHOR = {Birch, B.\thinspace{}J.},
    TITLE = {Elliptic curves over \protect{${\mathbf{Q}}$: {A}} progress report},
BOOKTITLE = {1969 Number Theory Institute (Proc. Sympos. Pure Math., Vol.
             XX, State Univ. New York, Stony Brook, N.Y., 1969)},
    PAGES = {396--400},
PUBLISHER = {Amer. Math. Soc.},
  ADDRESS = {Providence, R.I.},
     YEAR = {1971}
}

@incollection {birch:hecke_actions,
   AUTHOR = {Birch, B. J.},
    TITLE = {Hecke actions on classes of ternary quadratic forms},
BOOKTITLE = {Computational number theory (Debrecen, 1989)},
    PAGES = {191--212},
PUBLISHER = {de Gruyter},
  ADDRESS = {Berlin},
     YEAR = {1991},
  MRCLASS = {11E45 (11E20 11F11 11G05 11Y35)},
 MRNUMBER = {93i:11047},
   MRREVR = {Rainer Schulze-Pillot},
}

@proceedings {MR92i:11131,
    TITLE = {Computational number theory},
BOOKTITLE = {Proceedings of the colloquium held at Kossuth Lajos University,
             Debrecen, September 4--9, 1989},
   EDITOR = {Peth{\H{o}}, Attila and Pohst, Michael E. and Williams, Hugh C.
             and Zimmer, Horst G{\"u}nter},
PUBLISHER = {Walter de Gruyter \& Co.},
  ADDRESS = {Berlin},
     YEAR = {1991},
    PAGES = {xiv+342},
     ISBN = {3-11-012394-0},
  MRCLASS = {11Yxx (11-06)},
 MRNUMBER = {92i:11131},
}

@article {boston-lenstra-ribet,
   AUTHOR = {N. Boston and \protect{H.\thinspace{}W. Lenstra, Jr.} 
         and K.\thinspace{}A. Ribet},
    TITLE = {Quotients of group rings arising from two-dimensional
             representations},
  JOURNAL = {C. R. Acad. Sci. Paris S\'er. I Math.},
 FJOURNAL = {Comptes Rendus de l'Acad\'emie des Sciences. S\'erie I.
             Math\'ematique},
   VOLUME = {312},
     YEAR = {1991},
   NUMBER = {4},
    PAGES = {323--328},
     ISSN = {0764-4442},
    CODEN = {CASMEI},
}

@book{buhler:thesis,
   AUTHOR = {Buhler, J.\thinspace{}P.},
    TITLE = {Icosahedral \protect{G}alois representations},
     NOTE = {Lecture Notes in Mathematics, Vol. 654},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {1978},
    PAGES = {ii+143},
     ISBN = {3-540-08844-X},
}

@article{atkin-lehner,
   AUTHOR = {Atkin, A.\thinspace{}O.\thinspace{}L. and Lehner, J.},
    TITLE = {Hecke operators on \protect{$\Gamma \sb{0}(m)$}},
  JOURNAL = {Math. Ann.},
   VOLUME = {185},
     YEAR = {1970},
    PAGES = {134--160},
}

@article{galbraith,
   author = {Galbraith, S.\thinspace{}D.},
   title  = {Equations for modular curves},
   Year   = {1996},
 journal  = {Oxford Ph.D. thesis},
 pages    = {91 pp.}
}

@article{BRUE,
   author = {Brueggeman, S.},
   title  = {The non-existence of certain \protect{Galois} extensions 
      unramified outside 5},
   journal = {Journal of Number Theory},
   volume = {75},
   year   = {1999},
   pages  = {47--52}
}

@article{brumer:rank,
   AUTHOR = {Brumer, A.},
    TITLE = {The rank of \protect{${J}\sb 0({N})$}},
     NOTE = {Columbia University Number Theory Seminar (New York, 1992)},
  JOURNAL = {Ast\'erisque},
 FJOURNAL = {Ast\'erisque},
   NUMBER = {228},
     YEAR = {1995},
    PAGES = {3, 41--68},
     ISSN = {0303-1179},
}

@article {cassels:arithmeticIV,
   AUTHOR = {Cassels, J.\thinspace{}W.\thinspace{}S.},
    TITLE = {Arithmetic on curves of genus \protect{$1$}. {I}{V}. 
             {P}roof of the {H}auptvermutung},
  JOURNAL = {J. Reine Angew. Math.},
   VOLUME = {211},
     YEAR = {1962},
    PAGES = {95--112},
}

@article {cassels:arithmeticV,
   AUTHOR = {Cassels, J.\thinspace{}W.\thinspace{}S.},
    TITLE = {Arithmetic on curves of genus 1. {V}. {T}wo counterexamples},
  JOURNAL = {J. London Math. Soc.},
   VOLUME = {38},
     YEAR = {1963},
    PAGES = {244--248},
}

@article {cassels:diophantinecurve,
   AUTHOR = {Cassels, J.\thinspace{}W.\thinspace{}S.},
    TITLE = {Diophantine equations with special reference to elliptic
             curves},
  JOURNAL = {J. London Math. Soc.},
   VOLUME = {41},
     YEAR = {1966},
    PAGES = {193--291},
}

@incollection {cassels:global,
   AUTHOR = {Cassels, J.\thinspace{}W.\thinspace{}S.},
    TITLE = {Global fields},
BOOKTITLE = {Algebraic Number Theory (Proc. Instructional Conf., Brighton,
             1965)},
    PAGES = {42--84},
PUBLISHER = {Thompson, Washington, D.C.},
     YEAR = {1967},
}

@article{CAREARLY,
   author="Carayol, H.",
   title={Sur les \protect{repr\'esentations}
    \protect{$\ell$-adiques} \protect{associ\'ees}
     aux formes modulaires de \protect{Hilbert}},
   journal={Ann. scient. \protect{\'Ec.} Norm. Sup., 
            \protect{$4^{\rm eb}$ s\'erie}},
   volume={19},
   year={1986},
   pages={409--468}
}

@article{carayol:modell,
   author={Carayol, H.},
   title={Sur les \protect{repr\'esentations} galoisiennes
  modulo \protect{$\ell$ attach\'ees} aux formes modulaires},
  journal={Duke Math. J.},
   volume={59},
   year ={1989},
   pages ={785--801}
}

@article{coleman:monodromy,
   author = {Coleman, R.},
   title = {The {M}onodromy {P}airing},
    journal = {Asian Math. Journal},
   volume={4},
   year = {2000},
   pages = {315--330}
}

@article{cremona:onlinetables,
   author = {Cremona, J.\thinspace{}E.},
   title  = {Elliptic curves of conductor \protect{$\leq 12000$},\hfill\\
  {\sf http://www.maths.nott.ac.uk/personal/jec/ftp/data/}}
}

@book{cremona:algs,
   AUTHOR = {Cremona, J.\thinspace{}E.},
    TITLE = {Algorithms for modular elliptic curves},
  EDITION = {Second},
PUBLISHER = {Cambridge University Press},
  ADDRESS = {Cambridge},
     YEAR = {1997},
    PAGES = {vi+376},
     ISBN = {0-521-59820-6},
}


@article {cremona:periods,
   AUTHOR = {Cremona, J.\thinspace{}E.},
    TITLE = {Computing periods of cusp forms and modular elliptic curves},
  JOURNAL = {Experiment. Math.},
 FJOURNAL = {Experimental Mathematics},
   VOLUME = {6},
     YEAR = {1997},
   NUMBER = {2},
    PAGES = {97--107},
     ISSN = {1058-6458},
}

@article {gouvea:ordinary,
   AUTHOR = {Gouv\^ea, F.\thinspace{}Q.},
    TITLE = {On the ordinary {H}ecke algebra},
  JOURNAL = {J. Number Theory},
 FJOURNAL = {Journal of Number Theory},
   VOLUME = {41},
     YEAR = {1992},
   NUMBER = {2},
    PAGES = {178--198},
     ISSN = {0022-314X},
    CODEN = {JNUTA9},
}


@article{cremona:gammaone,
   AUTHOR = {Cremona, J.\thinspace{}E.},
    TITLE = {Modular symbols for \protect{$\Gamma\sb 1({N})$} 
             and elliptic curves with everywhere good reduction},
  JOURNAL = {Math. Proc. Cambridge Philos. Soc.},
 FJOURNAL = {Mathematical Proceedings of the Cambridge Philosophical
             Society},
   VOLUME = {111},
     YEAR = {1992},
   NUMBER = {2},
    PAGES = {199--218},
     ISSN = {0305-0041},
    CODEN = {MPCPCO},
}


@article {cremona-mazur,
   author= {Cremona, J.\thinspace{}E. and Mazur, B.},
     TITLE = {Visualizing elements in the {S}hafarevich-{T}ate group},
   JOURNAL = {Experiment. Math.},
  FJOURNAL = {Experimental Mathematics},
    VOLUME = {9},
      YEAR = {2000},
    NUMBER = {1},
     PAGES = {13--28},
      ISSN = {1058-6458},
   MRCLASS = {11Gxx (14Gxx)},
  MRNUMBER = {1 758 797},
}

@book {curtis-reiner,
   AUTHOR = {Curtis, C.\thinspace{}W. and Reiner, I.},
    TITLE = {Representation theory of finite groups and associative
             algebras},
     NOTE = {Pure and Applied Mathematics, Vol. XI},
PUBLISHER = {Interscience Publishers, a division of John Wiley \& Sons, New
             York-London},
     YEAR = {1962},
    PAGES = {xiv+685},
}

@incollection {darmon:serre,
   AUTHOR = {Darmon, Henri},
    TITLE = {Serre's conjectures},
BOOKTITLE = {Seminar on Fermat's Last Theorem (Toronto, ON, 1993--1994)},
    PAGES = {135--153},
PUBLISHER = {Amer. Math. Soc.},
  ADDRESS = {Providence, RI},
     YEAR = {1995},
  MRCLASS = {11F80 (11F11 11R32)},
 MRNUMBER = {96h:11048},
   MRREVR = {Dipendra Prasad},
}

@incollection{ddt,
   AUTHOR = {Darmon, H. and Diamond, F. and Taylor, R.},
    TITLE = {Fermat's last theorem},
BOOKTITLE = {Current developments in mathematics, 1995 (Cambridge, MA)},
    PAGES = {1--154},
PUBLISHER = {Internat. Press},
  ADDRESS = {Cambridge, MA},
     YEAR = {1994},
}

@article{eichler:quadratic,
   AUTHOR = {Eichler, M.},
    TITLE = {Quadratische \protect{F}ormen und \protect{M}odulfunktionen},
  JOURNAL = {Acta Arith.},
   VOLUME = {4},
     YEAR = {1958},
    PAGES = {217--239},
}

@article{eichler:ideal,
   author = {Eichler, M.},
   title  = {Uber die Idealklassenzahl total definiter
             Quaternionenalgebren}, 
   journal= {Math. Zeit.},
   volume = {43},
     year = {1937},
    pages = {102--109}
}

@book {knapp:elliptic,
   AUTHOR = {Knapp, A.\thinspace{}W.},
    TITLE = {Elliptic curves},
PUBLISHER = {Princeton University Press},
  ADDRESS = {Princeton, NJ},
     YEAR = {1992},
    PAGES = {xvi+427},
     ISBN = {0-691-08559-5},
}

@article {lang-tate,
   AUTHOR = {Lang, S. and Tate, J.},
    TITLE = {Principal homogeneous spaces over abelian varieties},
  JOURNAL = {Amer. J. Math.},
   VOLUME = {80},
     YEAR = {1958},
    PAGES = {659--684},
}

@article{shimizu:zeta,
   author = {Shimizu, H.},
    TITLE = {On zeta functions of quaternion algebras},
  JOURNAL = {Ann. of Math. (2)},
   VOLUME = {81},
     YEAR = {1965},
    PAGES = {166--193},
}


@inproceedings {deligne-rapoport,
   AUTHOR = {Deligne, P. and Rapoport, M.},
    TITLE = {Les sch\'emas de modules de courbes elliptiques},
BOOKTITLE = {Modular functions of one variable, II (Proc. Internat. Summer
             School, Univ. Antwerp, Antwerp, 1972)},
    PAGES = {143--316. Lecture Notes in Math., Vol. 349},
PUBLISHER = {Springer},
  ADDRESS = {Berlin},
     YEAR = {1973},
}

@article {serre:enseign,
   AUTHOR = {Serre, J-P.},
    TITLE = {Divisibilit\'e de certaines fonctions arithm\'etiques},
  JOURNAL = {Enseignement Math. (2)},
   VOLUME = {22},
     YEAR = {1976},
   NUMBER = {3-4},
    PAGES = {227--260},
  MRCLASS = {10H25 (10D05)},
 MRNUMBER = {55 #7958},
   MRREVR = {Larry J. Goldstein},
}

@inproceedings {serre:antwerp72,
   AUTHOR = {Serre, J-P.},
    TITLE = {Formes modulaires et fonctions z\^eta $p$-adiques},
BOOKTITLE = {Proceedings of the International Summer School, University of
             Antwerp, RUCA, July 17--August 3, 1972},
    PAGES = {191--268. Lecture Notes in Math., Vol. 350},
PUBLISHER = {Springer},
  ADDRESS = {Berlin},
     YEAR = {1973},
  MRCLASS = {10D05},
 MRNUMBER = {53 #7949a},
   MRREVR = {K.-B. Gundlach},
}


@book {MR48:2080,
    TITLE = {Modular functions of one variable. {I}{I}{I}},
BOOKTITLE = {Proceedings of the International Summer School, University of
             Antwerp, RUCA, July 17--August 3, 1972},
   EDITOR = {Kuyk, Willem and Serre, J.-P.},
     NOTE = {Lecture Notes in Mathematics, Vol. 350},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {1973},
    PAGES = {iv+350},
  MRCLASS = {10D05 (14K22)},
 MRNUMBER = {48 #2080},
}

% MR52:284,
@article {deligne-serre,
   AUTHOR = {Deligne, P. and Serre, J-P.},
    TITLE = {Formes modulaires de poids $1$},
  JOURNAL = {Ann. Sci. \'Ecole Norm. Sup. (4)},
   VOLUME = {7},
     YEAR = {1974},
    PAGES = {507--530 (1975)},
}

@article {diamond-kramer,
   AUTHOR = {Diamond, F. and Kramer, K.},
    TITLE = {Modularity of a family of elliptic curves},
  JOURNAL = {Math. Res. Lett.},
 FJOURNAL = {Mathematical Research Letters},
   VOLUME = {2},
     YEAR = {1995},
   NUMBER = {3},
    PAGES = {299--304},
     ISSN = {1073-2780},
}

@article{hijikata:trace,
   author={Hijikata, H.},
   title={Explicit formula of the traces    
      of \protect{H}ecke operators for
      \protect{$\Gamma_0(N)$}}, 
   journal={J. Math. Soc. Japan},
   number={1},
   volume={26},
   year={1974},
   pages={56--82}
}

@book {katzmazur,
   AUTHOR = {Katz, N.\thinspace{}M. and Mazur, B.},
    TITLE = {Arithmetic moduli of elliptic curves},
PUBLISHER = {Princeton University Press},
  ADDRESS = {Princeton, N.J.},
     YEAR = {1985},
    PAGES = {xiv+514},
     ISBN = {0-691-08349-5, 0-691-08352-5},
}


@incollection {lenstra-smit:explicit,
   AUTHOR = {de Smit, B. and Lenstra, H.\thinspace{}W.,Jr.},
    TITLE = {Explicit construction of universal deformation rings},
BOOKTITLE = {Modular forms and \protect{F}ermat's last theorem (Boston, MA, 1995)},
    PAGES = {313--326},
PUBLISHER = {Springer},
  ADDRESS = {New York},
     YEAR = {1997},
}


@article {livne:conductors, 
   AUTHOR = {Livn{\'e}, R.},
    TITLE = {On the conductors of mod \protect{$\ell$} 
              \protect{G}alois representations coming
             from modular forms},
  JOURNAL = {J. Number Theory},
 FJOURNAL = {Journal of Number Theory},
   VOLUME = {31},
     YEAR = {1989},
   NUMBER = {2},
    PAGES = {133--141},
     ISSN = {0022-314X},
    CODEN = {JNUTA9},
}

@incollection {mazur:deforming,
   AUTHOR = {Mazur, B.},
    TITLE = {Deforming \protect{G}alois representations},
BOOKTITLE = {Galois groups over \protect{${\bf Q}$} (Berkeley, CA, 1987)},
    PAGES = {385--437},
PUBLISHER = {Springer},
  ADDRESS = {New York},
     YEAR = {1989},
}

@article {mazur-ribet,
   AUTHOR = {Mazur, B. and Ribet, K.\thinspace{}A.},
    TITLE = {Two-dimensional representations in the arithmetic of modular
             curves},
     NOTE = {Courbes modulaires et courbes de Shimura (Orsay, 1987/1988)},
  JOURNAL = {Ast\'erisque},
 FJOURNAL = {Ast\'erisque},
   NUMBER = {196-197},
     YEAR = {1991},
    PAGES = {6, 215--255 (1992)},
     ISSN = {0303-1179},
}

@article {ono:partition,
   AUTHOR = {Ono, K. and Guo, L.},
    TITLE = {The partition function and the arithmetic of certain
             modular \protect{$L$}-functions},
  JOURNAL = {International Mathematical Research Notes},
   NUMBER = {},
     YEAR = {1999},
    PAGES = {},
}

@book {MR89b:14029,
    TITLE = {Arithmetic geometry},
   EDITOR = {Cornell, G. and Silverman, J.\thinspace{}H.},
     NOTE = {Papers from the conference held at the University of
             Connecticut, Storrs, Conn., July 30--August 10, 1984},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {New York},
     YEAR = {1986},
    PAGES = {xvi+353},
     ISBN = {0-387-96311-1},
}

@book{milne:duality,
   author = {Milne, J.\thinspace{}S.},
   TITLE = {Arithmetic duality theorems},
PUBLISHER = {Academic Press Inc.},
  ADDRESS = {Boston, Mass.},
     YEAR = {1986},
    PAGES = {x+421},
     ISBN = {0-12-498040-6},
}

@book {milne:etale,
   AUTHOR = {Milne, J.\thinspace{}S.},
    TITLE = {\'{E}tale cohomology},
PUBLISHER = {Princeton University Press},
  ADDRESS = {Princeton, N.J.},
     YEAR = {1980},
    PAGES = {xiii+323},
     ISBN = {0-691-08238-3},
  MRCLASS = {14-02 (14F20 18F99)},
 MRNUMBER = {81j:14002},
   MRREVR = {G. Horrocks},
}


@incollection {milne:abvars,
   AUTHOR = {Milne, J.\thinspace{}S.},
    TITLE = {Abelian varieties},
BOOKTITLE = {Arithmetic geometry (Storrs, Conn., 1984)},
    PAGES = {103--150},
PUBLISHER = {Springer},
  ADDRESS = {New York},
     YEAR = {1986},
}



@incollection {rosen:abvars,
   AUTHOR = {Rosen, M.},
    TITLE = {Abelian varieties over \protect{${\bf {C}}$}},
BOOKTITLE = {Arithmetic geometry (Storrs, Conn., 1984)},
    PAGES = {79--101},
PUBLISHER = {Springer},
  ADDRESS = {New York},
     YEAR = {1986},
}

@article{SAITO,
 author={Saito, T.},
 title={Modular forms and \protect{$p$}-adic {H}odge theory},
 journal={Invent. Math.},
 volume={129},
 year={1997},
 pages={607--620}}

@article {shimura:reciprocity,
   AUTHOR = {Shimura, G.},
    TITLE = {A reciprocity law in non-solvable extensions},
  JOURNAL = {J. Reine Angew. Math.},
   VOLUME = {221},
     YEAR = {1966},
    PAGES = {209--220},
}

@book {shimura:intro,
   AUTHOR = {Shimura, G.},
    TITLE = {Introduction to the arithmetic theory of automorphic functions},
     NOTE = {Reprint of the 1971 original,
             Kan Memorial Lectures, 1},
PUBLISHER = {Princeton University Press},
  ADDRESS = {Princeton, NJ},
     YEAR = {1994},
    PAGES = {xiv+271},
     ISBN = {0-691-08092-5},
}

@article {skinner-wiles:ordinary,
   AUTHOR = {Skinner, C.\thinspace{}M. and Wiles, A.\thinspace{}J.},
    TITLE = {Ordinary representations and modular forms},
  JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.},
 FJOURNAL = {Proceedings of the National Academy of Sciences of the United
             States of America},
   VOLUME = {94},
     YEAR = {1997},
   NUMBER = {20},
    PAGES = {10520--10527},
     ISSN = {0027-8424},
    CODEN = {PNASA6},
}


@article{wiles:cmi,
   AUTHOR = {Wiles, A.\thinspace{}J.},
    TITLE = {The {B}irch and {S}winnerton-{D}yer {C}onjecture},
  note = {\\\protect{\sf http://www.claymath.org/prize\_problems/birchsd.htm}},
     YEAR = {2000},
}

@article {wiles:fermat,
   AUTHOR = {Wiles, A.\thinspace{}J.},
    TITLE = {Modular elliptic curves and \protect{F}ermat's last theorem},
  JOURNAL = {Ann. of Math. (2)},
 FJOURNAL = {Annals of Mathematics. Second Series},
   VOLUME = {141},
     YEAR = {1995},
   NUMBER = {3},
    PAGES = {443--551},
     ISSN = {0003-486X},
    CODEN = {ANMAAH},
}

@article{breuil-conrad-diamond-taylor,
   AUTHOR = {Breuil, C. and Conrad, B. and Diamond, F. and Taylor, R.},
    TITLE = {On the modularity of elliptic curves over \protect{$\Q$}:
       {W}ild $3$-adic exercises},
  note = {\\\protect{\sf http://www.math.harvard.edu/HTML/Individuals/Richard\_Taylor.html}},
     YEAR = {2000},
}

@article{conrad-diamond-taylor:modularity,
   AUTHOR = {Conrad, B. and Diamond, F. and Taylor, R.},
    TITLE = {Modularity of certain potentially 
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             representations},
  JOURNAL = {J. Amer. Math. Soc.},
 FJOURNAL = {Journal of the American Mathematical Society},
   VOLUME = {12},
     YEAR = {1999},
   NUMBER = {2},
    PAGES = {521--567},
     ISSN = {0894-0347},
}




@article {merel:weil,
   AUTHOR = {Merel, L.},
    TITLE = {L'accouplement de {W}eil entre le sous-groupe de {S}himura et
             le sous-groupe cuspidal de ${J}\sb 0(p)$},
  JOURNAL = {J. Reine Angew. Math.},
 FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik},
   VOLUME = {477},
     YEAR = {1996},
    PAGES = {71--115},
     ISSN = {0075-4102},
    CODEN = {JRMAA8},
  MRCLASS = {11G18 (11F67)},
 MRNUMBER = {97f:11045},
   MRREVR = {Jan Nekov{\'a}{\v{r}}},
}

@article{merel:cyclo,
   author = {Merel, L.},
   title  = {Sur la nature non-cyclotomique des points
             d'ordre fini des courbes elliptiques},
  journal = {preprint},
    year  = {1999}
}

@inproceedings{merel:1585,
   AUTHOR = {Merel, L.},
    TITLE = {Universal \protect{F}ourier expansions of modular forms},
BOOKTITLE = {On {A}rtin's conjecture for odd 2-dimensional representations},
    PAGES = {59--94},
PUBLISHER = {Springer},
     YEAR = {1994},
}

@book {MR95i:11001,
    TITLE = {On {A}rtin's conjecture for odd 2-dimensional representations},
    EDITOR = {Frey, G.},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1994},
     PAGES = {viii+148},
      ISBN = {3-540-58387-4},
   MRCLASS = {11-06 (11F80)},
  MRNUMBER = {95i:11001},
      NOTE = {1585}
}

@article{bdsbt,
   author={Buzzard, K. and Dickinson, M.  
           and Shepherd-Barron, N. and Taylor, R.},
   title ={On icosahedral {A}rtin representations},
  JOURNAL = {
\protect{\sf http://www.math.harvard.edu/HTML/Individuals/Richard\_Taylor.html}},
   date = {2000}
}

@article{dickinson:thesis,
   author={Dickinson, M.},
   title={On the modularity of certain $2$-adic Galois representations},
   journal={Harvard Ph.D. thesis},
   year={2000}
}


@article{taylor-wiles:fermat,
   AUTHOR = {Taylor, R. and Wiles, A.\thinspace{}J.},
    TITLE = {Ring-theoretic properties of certain \protect{H}ecke algebras},
  JOURNAL = {Ann. of Math. (2)},
 FJOURNAL = {Annals of Mathematics. Second Series},
   VOLUME = {141},
     YEAR = {1995},
   NUMBER = {3},
    PAGES = {553--572},
     ISSN = {0003-486X},
    CODEN = {ANMAAH},
}

@article{ribet-stein:serre,
   author =  {Ribet, K.\thinspace{}A. and Stein, W.\thinspace{}A.},
   title  =  {Lectures on {S}erre's conjectures},
   journal = {IAS/Park City Mathematics Institute 1999}
}

@inproceedings{edixhoven:serre,
   author={Edixhoven, B.},
    TITLE = {Serre's conjecture},
BOOKTITLE = {Modular forms and \protect{F}ermat's last theorem (Boston, MA, 1995)},
    PAGES = {209--242},
PUBLISHER = {Springer},
  ADDRESS = {New York},
     YEAR = {1997},
}



@article{edixhoven:eisen,
   AUTHOR = {Edixhoven, B.},
    TITLE = {L'action de l'alg\`ebre de \protect{H}ecke sur les groupes de
             composantes des jacobiennes des courbes modulaires est
             ``\protect{E}isenstein''},
     NOTE = {Courbes modulaires et courbes de Shimura (Orsay, 1987/1988)},
  JOURNAL = {Ast\'erisque},
 FJOURNAL = {Ast\'erisque},
   NUMBER = {196--197},
     YEAR = {1991},
    PAGES = {7--8, 159--170 (1992)},
     ISSN = {0303-1179},
}


@book{jacquet-langlands,
   AUTHOR = {Jacquet, H. and Langlands, R.\thinspace{}P.},
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     NOTE = {Lecture Notes in Mathematics, Vol. 114},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {1970},
    PAGES = {vii+548},
}

@book {langlands:basechange,
   AUTHOR = {Langlands, R.\thinspace{}P.},
    TITLE = {Base change for \protect{${\rm {G}{L}}(2)$}},
PUBLISHER = {Princeton University Press},
  ADDRESS = {Princeton, N.J.},
     YEAR = {1980},
    PAGES = {vii+237},
     ISBN = {0-691-08263-4; 0-691-08272-3},
}


@inproceedings {langlands:antwerp2,
   AUTHOR = {Langlands, R.\thinspace{}P.},
    TITLE = {Modular forms and $\ell $-adic representations},
BOOKTITLE = {Proceedings of the International Summer 
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             Antwerp, RUCA, July 17--August 3, 1972},
   EDITOR = {Deligne, P. and Kuyk, W.},
    PAGES = {361--500. Lecture Notes in Math., Vol. 349},
PUBLISHER = {Springer},
  ADDRESS = {Berlin},
     YEAR = {1973},
  MRCLASS = {12A70 (10D15 14G10 22E50)},
 MRNUMBER = {50 #7095},
   MRREVR = {I. I. Pjateckii-Sapiro},
}

@article {tunnell:artin,
   AUTHOR = {Tunnell, J.},
    TITLE = {Artin's conjecture for representations of octahedral type},
  JOURNAL = {Bull. Amer. Math. Soc. (N.S.)},
 FJOURNAL = {American Mathematical Society. Bulletin. New Series},
   VOLUME = {5},
     YEAR = {1981},
   NUMBER = {2},
    PAGES = {173--175},
     ISSN = {0002-9904},
    CODEN = {BAMOAD},
}

@article {edixhoven:weight,
   AUTHOR = {Edixhoven, B.},
    TITLE = {The weight in \protect{S}erre's conjectures on modular forms},
  JOURNAL = {Invent. Math.},
 FJOURNAL = {Inventiones Mathematicae},
   VOLUME = {109},
     YEAR = {1992},
   NUMBER = {3},
    PAGES = {563--594},
     ISSN = {0020-9910},
    CODEN = {INVMBH},
}

@article {jordan-livne:epsilon,
   AUTHOR = {Jordan, B.\thinspace{}W. and Livn{\'e}, R.},
    TITLE = {Conjecture ``epsilon'' for weight \protect{$k>2$}},
  JOURNAL = {Bull. Amer. Math. Soc. (N.S.)},
 FJOURNAL = {American Mathematical Society. Bulletin. New Series},
   VOLUME = {21},
     YEAR = {1989},
   NUMBER = {1},
    PAGES = {51--56},
     ISSN = {0273-0979},
    CODEN = {BAMOAD},
}

@article {edixcole,
   AUTHOR = {Coleman, R.\thinspace{}F. and Edixhoven, B.},
    TITLE = {On the semi-simplicity of the 
             \protect{${U}\sb p$}-operator on modular forms},
  JOURNAL = {Math. Ann.},
 FJOURNAL = {Mathematische Annalen},
   VOLUME = {310},
     YEAR = {1998},
   NUMBER = {1},
    PAGES = {119--127},
     ISSN = {0025-5831},
    CODEN = {MAANA},
}



@article {faltings-jordan,
   AUTHOR = {Faltings, G. and Jordan, B.\thinspace{}W.},
    TITLE = {Crystalline cohomology and \protect{${\rm {G}{L}}(2,{\bf {Q}})$}},
  JOURNAL = {Israel J. Math.},
 FJOURNAL = {Israel Journal of Mathematics},
   VOLUME = {90},
     YEAR = {1995},
   NUMBER = {1-3},
    PAGES = {1--66},
     ISSN = {0021-2172},
    CODEN = {ISJMAP},
}


@article {coleman-edixhoven,
   AUTHOR = {Coleman, R.\thinspace{}F. and Edixhoven, B.},
    TITLE = {On the semi-simplicity of the \protect{${U}\sb p$}-operator 
             on modular forms},
  JOURNAL = {Math. Ann.},
 FJOURNAL = {Mathematische Annalen},
   VOLUME = {310},
     YEAR = {1998},
   NUMBER = {1},
    PAGES = {119--127},
     ISSN = {0025-5831},
    CODEN = {MAANA},
  MRCLASS = {11F25 (11F11 11F33 11F85)},
 MRNUMBER = {99b:11043},
   MRREVR = {Alexey A. Panchishkin},
}

@article {coleman-voloch,
   AUTHOR = {Coleman, R.\thinspace{}F. and Voloch, J.\thinspace{}F.},
    TITLE = {Companion forms and \protect{K}odaira-\protect{S}pencer theory},
  JOURNAL = {Invent. Math.},
 FJOURNAL = {Inventiones Mathematicae},
   VOLUME = {110},
     YEAR = {1992},
   NUMBER = {2},
    PAGES = {263--281},
     ISSN = {0020-9910},
    CODEN = {INVMBH},
}



@article {faltings-finiteness,
   AUTHOR = {Faltings, G.},
    TITLE = {\protect{Endlichkeitss\"atze f\"ur} abelsche 
             \protect{V}ariet\"aten \"uber
             \protect{Z}ahlk\"orpern},
  JOURNAL = {Invent. Math.},
 FJOURNAL = {Inventiones Mathematicae},
   VOLUME = {73},
     YEAR = {1983},
   NUMBER = {3},
    PAGES = {349--366},
     ISSN = {0020-9910},
    CODEN = {INVMBH},
}







@article {empirical,
   AUTHOR = {Flynn, E.\thinspace{}V. and \protect{Lepr\'{e}vost}, F. 
             and Schaefer, E.\thinspace{}F. and Stein, W.\thinspace{}A.
             and Stoll, M. and Wetherell, J.\thinspace{}L.},
     TITLE = {Empirical evidence for the {B}irch and {S}winnerton-{D}yer
              conjectures for modular {J}acobians of genus 2 curves},
   JOURNAL = {Math. Comp.},
  FJOURNAL = {Mathematics of Computation},
    VOLUME = {70},
      YEAR = {2001},
    NUMBER = {236},
     PAGES = {1675--1697 (electronic)},
      ISSN = {0025-5718},
     CODEN = {MCMPAF},
   MRCLASS = {},
  MRNUMBER = {1 836 926},
}

@inproceedings{frey:boston,
   AUTHOR = {Frey, G.},
    TITLE = {On ternary equations of \protect{F}ermat type and relations with
             elliptic curves},
BOOKTITLE = {Modular forms and \protect{F}ermat's last theorem (Boston, MA, 1995)},
    PAGES = {527--548},
PUBLISHER = {Springer},
  ADDRESS = {New York},
     YEAR = {1997},
  crossref="boston"
}



@incollection{frey-muller,
   AUTHOR = {Frey, G. and M{\"u}ller, M.},
    TITLE = {Arithmetic of modular curves and applications},
BOOKTITLE = {Algorithmic algebra and number theory (Heidelberg, 1997)},
    PAGES = {11--48},
PUBLISHER = {Springer},
  ADDRESS = {Berlin},
     YEAR = {1999}
}


@incollection {birch:cyclo,
   AUTHOR = {Birch, B.\thinspace{}J.},
    TITLE = {Cyclotomic fields and {K}ummer extensions},
BOOKTITLE = {Algebraic Number Theory (Proc. Instructional Conf., Brighton,
             1965)},
    PAGES = {85--93},
PUBLISHER = {Thompson, Washington, D.C.},
     YEAR = {1967},
}

@incollection {frohlich:local,
   AUTHOR = {Fr{\"o}hlich, A.},
    TITLE = {Local fields},
BOOKTITLE = {Algebraic Number Theory (Proc. Instructional Conf., Brighton,
             1965) },
    PAGES = {1--41},
PUBLISHER = {Thompson, Washington, D.C.},
     YEAR = {1967},
}

@proceedings {MR91k:11003,
    TITLE = {$L$-functions and arithmetic},
BOOKTITLE = {Proceedings of the London Mathematical Society Symposium held
             at the University of Durham, Durham, June 30--July 11, 1989},
   EDITOR = {Coates, J. and Taylor, M. J.},
PUBLISHER = {Cambridge University Press},
  ADDRESS = {Cambridge},
     YEAR = {1991},
    PAGES = {ix+392},
     ISBN = {0-521-38619-5},
}


@article {lichtenbaum:duality,
   AUTHOR = {Lichtenbaum, S.},
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  JOURNAL = {Invent. Math.},
   VOLUME = {7},
     YEAR = {1969},
    PAGES = {120--136},
}

@article {lichtenbaum:curves,
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     TITLE = {Curves over discrete valuation rings},
   JOURNAL = {Amer. J. Math.},
    VOLUME = {90},
      YEAR = {1968},
     PAGES = {380--405},
   MRCLASS = {14.20},
  MRNUMBER = {37 \#6284},
MRREVIEWER = {J.-E. Bertin},
}



@article {bump-friedberg-hoffstein,
   AUTHOR = {Bump, D. and Friedberg, S. and Hoffstein, J.},
    TITLE = {Eisenstein series on the metaplectic group and nonvanishing
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             and their derivatives},
  JOURNAL = {Ann. of Math. (2)},
 FJOURNAL = {Annals of Mathematics. Second Series},
   VOLUME = {131},
     YEAR = {1990},
   NUMBER = {1},
    PAGES = {53--127},
     ISSN = {0003-486X},
    CODEN = {ANMAAH},
}

@incollection {gross:kolyvagin,
   AUTHOR = {Gross, B.\thinspace{}H.},
    TITLE = {Kolyvagin's work on modular elliptic curves},
BOOKTITLE = {$L$-functions and arithmetic (Durham, 1989)},
    PAGES = {235--256},
PUBLISHER = {Cambridge Univ. Press},
  ADDRESS = {Cambridge},
     YEAR = {1991},
}



@article {gross:tameness,
   AUTHOR = {Gross, B.\thinspace{}H.},
    TITLE = {A tameness criterion for \protect{G}alois 
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  JOURNAL = {Duke Math. J.},
 FJOURNAL = {Duke Mathematical Journal},
   VOLUME = {61},
     YEAR = {1990},
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    PAGES = {445--517},
     ISSN = {0012-7094},
    CODEN = {DUMJAO},
}

@book {grothendieck:monodromie,
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    TITLE = {Groupes de monodromie en 
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     NOTE = {S\'eminaire de G\'eom\'etrie Alg\'ebrique du Bois-Marie
             1967--1969 (SGA 7 I),
             Dirig\'e par A. Grothendieck. Avec la collaboration de M.
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PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {1972},
    PAGES = {viii+523},
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@book {hartshorne,
   AUTHOR = {Hartshorne, R.},
    TITLE = {Algebraic {G}eometry},
     NOTE = {Graduate Texts in Mathematics, No. 52},
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  ADDRESS = {New York},
     YEAR = {1977},
    PAGES = {xvi+496},
     ISBN = {0-387-90244-9},
}


@article {igusa:fibre,
   AUTHOR = {Igusa, J.},
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  JOURNAL = {Amer. J. Math.},
   VOLUME = {78},
     YEAR = {1956},
    PAGES = {171--199},
}




@article {jochnowitz:duke,
   AUTHOR = {Jochnowitz, N.},
    TITLE = {The index of the {H}ecke ring, ${T}\sb{k}$, in the ring of
             integers of \protect{${T}\sb{k}\otimes {\bf {Q}}$}},
  JOURNAL = {Duke Math. J.},
 FJOURNAL = {Duke Mathematical Journal},
   VOLUME = {46},
     YEAR = {1979},
   NUMBER = {4},
    PAGES = {861--869},
     ISSN = {0012-7094},
    CODEN = {DUMJAO},
  MRCLASS = {10D12},
 MRNUMBER = {80k:10023},
   MRREVR = {Henri Cohen},
}

@article {jochnowitz:local,
   AUTHOR = {Jochnowitz, N.},
    TITLE = {A study of the local components of the 
             \protect{H}ecke algebra mod \protect{$\ell$}},
  JOURNAL = {Trans. Amer. Math. Soc.},
 FJOURNAL = {Transactions of the American Mathematical Society},
   VOLUME = {270},
     YEAR = {1982},
   NUMBER = {1},
    PAGES = {253--267},
     ISSN = {0002-9947},
    CODEN = {TAMTAM},
}

@article{kohel:hecke,
  author="Kohel, D.\thinspace{}R.",
  title="Hecke Module Structure of Quaternions", 
  journal="In K. Miyake, ed., {\em Class Field Theory -- Its Centenary and Prospect},
  The Advanced Studies in Pure Mathematics Series, Math Soc. Japan."
}

@article{kohel:computing,
  author = "Kohel, D.\thinspace{}R.",
   title = "Computing modular curves via quaternions",
  journal = "Fourth CANT Conference",
    year = 1997
}

@inproceedings{kohel-stein:ants4,
  author = "Kohel, D.\thinspace{}R. and Stein, W.\thinspace{}A.",
  title = "Component {G}roups of {Q}uotients of \protect{$J_0(N)$}",
  booktitle={Proceedings of the 4th International Symposium (ANTS-IV),
             Leiden, Netherlands, July 2--7, 2000},
  publisher={Springer},
  address={Berlin},
   year={2000}
}

@proceedings {MR2000g:11002,
    TITLE = {Algorithmic number theory},
BOOKTITLE = {Proceedings of the 3rd International Symposium (ANTS-III) held
             at Reed College, Portland, OR, June 21--25, 1998},
   EDITOR = {Buhler, J. P.},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {1998},
    PAGES = {x+640},
     ISBN = {3-540-64657-4},
  MRCLASS = {11-06 (11Yxx)},
 MRNUMBER = {2000g:11002},
}

@proceedings {MR2000g:11002,
    TITLE = {Algorithmic number theory},
BOOKTITLE = {Proceedings of the 4th International Symposium (ANTS-IV),
             Leiden, The Netherlands, July 2--7, 2000},
   EDITOR = {Wieb Bosma},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {2000},
    PAGES = {},
     ISBN = {3540676953}
}

@article {cerednik,
   AUTHOR = {{\v{C}}erednik, I.\thinspace{}V.},
    TITLE = {Uniformization of algebraic curves by discrete arithmetic
             subgroups of \protect{${\rm {P}{G}{L}}\sb{2}(k\sb{w})$} 
             with compact quotient spaces},
  JOURNAL = {Mat. Sb. (N.S.)},
   VOLUME = {100(142)},
     YEAR = {1976},
   NUMBER = {1},
    PAGES = {59--88, 165},
}

@article {magma,
   AUTHOR = {Bosma, W. and Cannon, J. and Playoust, C.},
    TITLE = {The {M}agma algebra system. {I}. {T}he user language},
     NOTE = {Computational algebra and number theory (London, 1993)},
  JOURNAL = {J. Symbolic Comput.},
 FJOURNAL = {Journal of Symbolic Computation},
   VOLUME = {24},
     YEAR = {1997},
   NUMBER = {3-4},
    PAGES = {235--265},
     ISSN = {0747-7171},
  MRCLASS = {68Q40},
 MRNUMBER = {1 484 478},
}

@article {drinfeld:coverings,
   AUTHOR = {Drinfeld, V.\thinspace{}G.},
    TITLE = {Coverings of \protect{$p$-adic} symmetric domains},
  JOURNAL = {Funkcional. Anal. i Prilov zen.},
   VOLUME = {10},
     YEAR = {1976},
   NUMBER = {2},
    PAGES = {29--40},
}

@article{koike:conjtwist,
  author="Koike, M.",
  title="On certain abelian varieties obtained from new forms of 
         weight $2$ on \protect{$\Gamma_0(3^4)$ and $\Gamma_0(3^5)$}",
  journal={Nogoya Math. J.},
  volume={62},
  year={1976},
  pages={29--39}
}


@inproceedings {kolyvagin:mordellweil,
   AUTHOR = {Kolyvagin, V.\thinspace{}A.},
    TITLE = {On the {M}ordell-{W}eil group and the {S}hafarevich-{T}ate
             group of modular elliptic curves},
BOOKTITLE = {Proceedings of the International Congress of Mathematicians,
             Vol.\ I, II (Kyoto, 1990)},
    PAGES = {429--436},
PUBLISHER = {Math. Soc. Japan},
  ADDRESS = {Tokyo},
     YEAR = {1991},
  MRCLASS = {11G40 (11G05 14G10)},
 MRNUMBER = {93c:11046},
   MRREVR = {John Jones},
}

@incollection {kolyvagin:structureofsha,
   AUTHOR = {Kolyvagin, V.\thinspace{}A.},
    TITLE = {On the structure of {S}hafarevich-{T}ate groups},
BOOKTITLE = {Algebraic geometry (Chicago, IL, 1989)},
    PAGES = {94--121},
PUBLISHER = {Springer},
  ADDRESS = {Berlin},
     YEAR = {1991},
}





@proceedings {MR93d:14004,
    TITLE = {Algebraic geometry},
BOOKTITLE = {Proceedings of the US-USSR Symposium held at the University of
             Chicago, Chicago, Illinois, June 20--July 14, 1989},
   EDITOR = {Bloch, S. and Dolgachev, I. and Fulton, W.},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {1991},
    PAGES = {viii+300},
     ISBN = {3-540-54456-9},
}


@article{kolyvagin-logachev:totallyreal,
   author = "Kolyvagin, V.\thinspace{}A. and Logachev, D.\thinspace{}Y.",
   title = "Finiteness of \protect{$\Sha$} over totally real fields",
   journal={Math. USSR Izvestiya},
   volume ={39}, 
   year = {1992},
   number = {1},
   pages={829--853}
}

@article{kolyvagin-logachev:finiteness,
   AUTHOR = {Kolyvagin, V.\thinspace{}A. and Logachev, D.\thinspace{}Y.},
    TITLE = {Finiteness of the \protect{S}hafarevich-\protect{T}ate group and the group of
             rational points for some modular abelian varieties},
  JOURNAL = {Algebra i Analiz},
 FJOURNAL = {Algebra i Analiz},
   VOLUME = {1},
     YEAR = {1989},
   NUMBER = {5},
    PAGES = {171--196},
     ISSN = {0234-0852},
}

@book {lang:ant,
   AUTHOR = {Lang, S.},
    TITLE = {Algebraic number theory},
  EDITION = {Second},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {New York},
     YEAR = {1994},
    PAGES = {xiv+357},
     ISBN = {0-387-94225-4},
}

@book {lang:algebra,
   AUTHOR = {Lang, S.},
    TITLE = {Algebra},
  EDITION = {Third},
PUBLISHER = {Addison-Wesley Publishing Co., Reading, Mass.},
     YEAR = {1993},
    PAGES = {xv+912},
     ISBN = {0-201-55540-9},
}

@book {miyake,
   AUTHOR = {Miyake, T.},
    TITLE = {Modular forms},
     NOTE = {Translated from the Japanese by Yoshitaka Maeda},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {1989},
    PAGES = {x+335},
     ISBN = {3-540-50268-8},
}


@proceedings {MR86e:00018,
    TITLE = {Arbeitstagung {B}onn 1984},
BOOKTITLE = {Proceedings of the 25th mathematical workshop held at the
             Max-Planck-Institut f\"ur Mathematik, Bonn, June 15--22, 1984},
   EDITOR = {Hirzebruch, F. and Schwermer, J. and Suter, S.},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {1985},
    PAGES = {iii+481},
     ISBN = {3-540-15195-8},
}


@article {shafarevich:exp,
   AUTHOR = {Shafarevich, I.\thinspace{}R.},
    TITLE = {Exponents of elliptic curves},
  JOURNAL = {Dokl. Akad. Nauk SSSR (N.S.)},
   VOLUME = {114},
     YEAR = {1957},
    PAGES = {714--716},
}

@article {zagier:parametrizations,
   AUTHOR = {Zagier, D.},
    TITLE = {Modular parametrizations of elliptic curves},
  JOURNAL = {Canad. Math. Bull.},
 FJOURNAL = {Canadian Mathematical Bulletin},
   VOLUME = {28},
     YEAR = {1985},
   NUMBER = {3},
    PAGES = {372--384},
     ISSN = {0008-4395},
    CODEN = {CMBUA3},
  MRCLASS = {11G05 (11F11 14G25 14K07 14K15)},
 MRNUMBER = {86m:11041},
   MRREVR = {C.-G. Schmidt},
}

@article {gross-zagier,
    author = {Gross, B. and Zagier, D.},
    TITLE = {Heegner points and derivatives of \protect{${L}$}-series},
  JOURNAL = {Invent. Math.},
 FJOURNAL = {Inventiones Mathematicae},
   VOLUME = {84},
     YEAR = {1986},
   NUMBER = {2},
    PAGES = {225--320},
     ISSN = {0020-9910},
    CODEN = {INVMBH},
  MRCLASS = {11G40 (11F11 11G05 14G10)},
 MRNUMBER = {87j:11057},
   MRREVR = {Loren D. Olson},
}


@article {gross-kohnen-zagier,
   AUTHOR = {Gross, B. and Kohnen, W. and Zagier, D.},
    TITLE = {Heegner points and derivatives of ${L}$-series. {I}{I}},
  JOURNAL = {Math. Ann.},
 FJOURNAL = {Mathematische Annalen},
   VOLUME = {278},
     YEAR = {1987},
   NUMBER = {1-4},
    PAGES = {497--562},
     ISSN = {0025-5831},
    CODEN = {MAANA3},
  MRCLASS = {11G40 (11F30 11G05 11R29 14G10)},
 MRNUMBER = {89i:11069},
   MRREVR = {Lawrence Washington},
}

@incollection {zagier:modular,
   AUTHOR = {Zagier, D.},
    TITLE = {Modular points, modular curves, modular surfaces and modular
             forms},
BOOKTITLE = {Workshop Bonn 1984 (Bonn, 1984)},
    PAGES = {225--248},
PUBLISHER = {Springer},
  ADDRESS = {Berlin},
     YEAR = {1985},
}

@book {lang:modular,
   AUTHOR = {Lang, S.},
    TITLE = {Introduction to modular forms},
     NOTE = {With appendixes by D. Zagier and W. Feit,
             Corrected reprint of the 1976 original},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {1995},
    PAGES = {x+261},
     ISBN = {3-540-07833-9},
}


@article {lorenzini:abvarred,
   AUTHOR = {Lorenzini, D.\thinspace{}J.},
   title = "On the Jacobian of the Modular Curve \protect{$X_0(N)$}",
   journal = "preprint"
}
@article {lorenzini:compgrp,
   AUTHOR = {Lorenzini, D.\thinspace{}J.},
    TITLE = {On the group of components of a \protect{N}\'eron model},
  JOURNAL = {J. Reine Angew. Math.},
 FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik},
   VOLUME = {445},
     YEAR = {1993},
    PAGES = {109--160},
     ISSN = {0075-4102},
    CODEN = {JRMAA8},
}

@article{manin:cyclo,
   AUTHOR = {Manin, J.\thinspace{}I.},
    TITLE = {Cyclotomic fields and modular curves},
  JOURNAL = {Russian Math. Surveys},
   VOLUME = {26},
     YEAR = {1971},
   NUMBER = {6},
    PAGES = {7--78},
}


@article {manin:parabolic,
   AUTHOR = {Manin, J.\thinspace{}I.},
    TITLE = {Parabolic points and zeta functions of modular curves},
  JOURNAL = {Izv. Akad. Nauk SSSR Ser. Mat.},
   VOLUME = {36},
     YEAR = {1972},
    PAGES = {19--66},
  MRCLASS = {14G10 (10D15 14H25)},
 MRNUMBER = {47 \#3396},
   MRREVR = {K.-B. Gundlach},
}

@book{rubin:book,
   Author={Rubin, K.},
  title = {{E}uler {S}ystems},
  note = {{A}nnals of {M}athematics {S}tudies {\bf 147},
          \protect{\sf http://math.Stanford.EDU/\~{ }rubin/weyl.html}},
  publisher = {Princeton University Press},
  year = {Spring 2000}
}
@article {rubin:main-conjectures,
   AUTHOR = {Rubin, K.},
    TITLE = {The ``main conjectures'' of {I}wasawa theory for imaginary
             quadratic fields},
  JOURNAL = {Invent. Math.},
 FJOURNAL = {Inventiones Mathematicae},
   VOLUME = {103},
     YEAR = {1991},
   NUMBER = {1},
    PAGES = {25--68},
     ISSN = {0020-9910},
    CODEN = {INVMBH},
  MRCLASS = {11R23 (11G05 11G40)},
 MRNUMBER = {92f:11151},
   MRREVR = {M. A. Kenku},
}



@incollection {rubin:kolyvagin,
   AUTHOR = {Rubin, K.},
    TITLE = {The work of {K}olyvagin on the arithmetic of elliptic curves},
BOOKTITLE = {Arithmetic of complex manifolds (Erlangen, 1988)},
    PAGES = {128--136},
PUBLISHER = {Springer},
  ADDRESS = {Berlin},
     YEAR = {1989},
}

@article {rubin:cmsha,
   AUTHOR = {Rubin, Karl},
    TITLE = {Tate-{S}hafarevich groups and ${L}$-functions of elliptic
             curves with complex multiplication},
  JOURNAL = {Invent. Math.},
 FJOURNAL = {Inventiones Mathematicae},
   VOLUME = {89},
     YEAR = {1987},
   NUMBER = {3},
    PAGES = {527--559},
     ISSN = {0020-9910},
    CODEN = {INVMBH},
}



@proceedings {MR90h:14001,
    TITLE = {Arithmetic of complex manifolds},
BOOKTITLE = {Proceedings of the conference held at the University of
             Erlangen, Erlangen, May 27--31, 1988},
   EDITOR = {Barth, W. P. and Lange, H.},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {1989},
    PAGES = {vi+171},
     ISBN = {3-540-51729-4},
}





@ARTICLE{mazur:eisenstein,
   AUTHOR = {Mazur, B.},
    TITLE = {Modular curves and the \protect{Eisenstein} ideal},
  JOURNAL = {Inst. Hautes \'Etudes Sci. Publ. Math.},
 FJOURNAL = {Institut des Hautes \'Etudes Scientifiques. Publications
             Math\'ematiques},
   NUMBER = {47},
     YEAR = {1977},
    PAGES = {33--186 (1978)},
     ISSN = {0073-8301},
    CODEN = {PMIHA6},
}

@article{mazur:tower,
   AUTHOR = {Mazur, B.},
    TITLE = {Rational points of abelian varieties with values in towers of
             number fields},
  JOURNAL = {Invent. Math.},
   VOLUME = {18},
     YEAR = {1972},
    PAGES = {183--266},
}

@article{mazur:rational,
   AUTHOR = {Mazur, B.},
    TITLE = {Rational isogenies of prime degree (with an appendix by {D}.
             {G}oldfeld)},
  JOURNAL = {Invent. Math.},
 FJOURNAL = {Inventiones Mathematicae},
   VOLUME = {44},
     YEAR = {1978},
   NUMBER = {2},
    PAGES = {129--162},
     ISSN = {0020-9910},
    CODEN = {INVMBH},
}

@article {mazur:towers,
   AUTHOR = {Mazur, B.},
    TITLE = {Rational points of abelian varieties with values in towers of
             number fields},
  JOURNAL = {Invent. Math.},
   VOLUME = {18},
     YEAR = {1972},
    PAGES = {183--266},
  MRCLASS = {14G25 (14K15)},
 MRNUMBER = {56 #3020},
   MRREVR = {J.\thinspace{}S. Milne},
}


@article{mazur:arizona, 
   author="Mazur, B.",
   title ="Three lectures about the arithmetic 
           of elliptic curves.",
   journal="To appear in the proceedings from the Arizona Southwest Geometry Winter School",
   year=1998
}
 
@article{mazur:visord3,
   author="Mazur, B.",
   title="Visualizing elements of order three 
          in the Shafarevich-Tate group.",
   journal="preprint", 
   year=1998
}



@article{mestre:graphs,
   AUTHOR = {Mestre, J.-F.},
    TITLE = {La m\'ethode des graphes. \protect{Exemples} et applications},
JOURNAL = {Proceedings of the international conference on class numbers
             and fundamental units of algebraic number fields (Katata)},
    PAGES = {217--242},
PUBLISHER = {Nagoya Univ.},
  ADDRESS = {Nagoya},
     YEAR = {1986},
}

@article{mestre-oesterle,
   AUTHOR = {Mestre, J.-F. and Oesterl{\'e}, J.},
    TITLE = {Method of graphs (unpublished manuscript)}
}

@article {raynaud:ihes,
   AUTHOR = {Raynaud, M.},
    TITLE = {Sp\'ecialisation du foncteur de {P}icard},
  JOURNAL = {Inst. Hautes \'Etudes Sci. Publ. Math. No.},
   VOLUME = {38},
     YEAR = {1970},
    PAGES = {27--76},
  MRCLASS = {14.55},
 MRNUMBER = {44 #227},
   MRREVR = {R. T. Hoobler},
}

@article{raynaud,
   author = {Raynaud},
   title  = {I'm not sure which paper}
}

@book {mumford:abvars,
   AUTHOR = {Mumford, D.},
    TITLE = {Abelian varieties},
     NOTE = {Tata Institute of Fundamental Research Studies in Mathematics,
             No. 5 },
PUBLISHER = {Published for the Tata Institute of Fundamental Research,
             Bombay},
     YEAR = {1970},
    PAGES = {viii+242},
}

@incollection {sturm:cong,
   AUTHOR = {Sturm, J.},
    TITLE = {On the congruence of modular forms},
BOOKTITLE = {Number theory (New York, 1984--1985)},
    PAGES = {275--280},
PUBLISHER = {Springer},
  ADDRESS = {Berlin},
     YEAR = {1987},
}

@proceedings {MR87m:11004,
    TITLE = {Number theory},
BOOKTITLE = {Proceedings of the seminar held at the City University of New
             York, New York, 1984--1985},
   EDITOR = {Chudnovsky, D.\thinspace{}V. and 
                Chudnovsky, G.\thinspace{}V. 
                  and Cohn, H. and
                  Nathanson, M.\thinspace{}B.},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {1987},
    PAGES = {vi+324},
     ISBN = {3-540-17669-1},
}

@book {MR99f:00041,
    TITLE = {S\'eminaire {B}ourbaki. {V}ol. 9},
     NOTE = {Ann\'ees 1964/65-1965/66. [Years 1964/65-1965/66],
             Expos\'es 277--312,
             Reprint of the edition published by W. A. Benjamin, New
             York-Amsterdam, 1966 [MR {\bf 33} \#5420l; MR {\bf 34} \#5605]},
PUBLISHER = {Soci\'et\'e Math\'ematique de France},
  ADDRESS = {Paris},
     YEAR = {1995},
    PAGES = {iv+531},
     ISBN = {2-85629-042-6},
}

@incollection {tate:bsd,
   AUTHOR = {Tate, J.},
    TITLE = {On the conjectures of {B}irch and {S}winnerton-{D}yer and a
             geometric analog},
BOOKTITLE = {S\'eminaire Bourbaki, Vol.\ 9},
    PAGES = {Exp.\ No.\ 306, 415--440},
PUBLISHER = {Soc. Math. France},
  ADDRESS = {Paris},
     YEAR = {1995},
}



@book {mumford:geometric,
   AUTHOR = {Mumford, D. and Fogarty, J. and Kirwan, F.},
    TITLE = {Geometric invariant theory},
  EDITION = {Third},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {1994},
    PAGES = {xiv+292},
     ISBN = {3-540-56963-4},
}

@inproceedings {queen,
   AUTHOR = {Queen, C.},
    TITLE = {The existence of \protect{$p$}-adic 
              \protect{A}belian 
              \protect{${L}$}-functions},
BOOKTITLE = {Number theory and algebra},
    PAGES = {263--288},
PUBLISHER = {Academic Press},
  ADDRESS = {New York},
     YEAR = {1977},
}

@book {MR56:11675,
    TITLE = {Number theory and algebra},
   EDITOR = {Zassenhaus, H.},
     NOTE = {Collected papers dedicated to Henry B. Mann, Arnold E. Ross,
             and Olga Taussky-Todd},
PUBLISHER = {Academic Press [Harcourt Brace Jovanovich Publishers]},
  ADDRESS = {New York},
     YEAR = {1977},
    PAGES = {x1vi+393},
     ISBN = {0-12-776350-3.},
}

@article {ribet:galoissurvey,
   AUTHOR = {Ribet, K.\thinspace{}A.},
    TITLE = {Galois representations and modular forms},
  JOURNAL = {Bull. Amer. Math. Soc. (N.S.)},
 FJOURNAL = {American Mathematical Society. Bulletin. New Series},
   VOLUME = {32},
     YEAR = {1995},
   NUMBER = {4},
    PAGES = {375--402},
     ISSN = {0273-0979},
    CODEN = {BAMOAD},
}

@book {MR90j:11004,
    TITLE = {S\'eminaire de {T}h\'eorie des {N}ombres, {P}aris 1987--88},
   EDITOR = {Goldstein, Catherine},
     NOTE = {Papers from the seminar held in Paris, 1987--88},
PUBLISHER = {Birkh\"auser Boston Inc.},
  ADDRESS = {Boston, MA},
     YEAR = {1990},
    PAGES = {viii+350},
     ISBN = {0-8176-3458-4},
}

@incollection {ribet:raising,
   AUTHOR = {Ribet, K.\thinspace{}A.},
    TITLE = {Raising the levels of modular representations},
BOOKTITLE = {S\'eminaire de Th\'eorie des Nombres, Paris 1987--88},
    PAGES = {259--271},
PUBLISHER = {Birkh\"auser Boston},
  ADDRESS = {Boston, MA},
     YEAR = {1990},
}

@inproceedings {ribet:galoisattached,
   AUTHOR = {Ribet, K.\thinspace{}A.},
    TITLE = {Galois representations attached to eigenforms with
             \protect{N}ebentypus},
BOOKTITLE = {Modular functions of one variable, V (Proc. Second Internat.
             Conf., Univ. Bonn, Bonn, 1976)},
    PAGES = {17--51. Lecture Notes in Math., Vol. 601},
PUBLISHER = {Springer},
  ADDRESS = {Berlin},
     YEAR = {1977},
}

@article {katz:annals75,
   AUTHOR = {Katz, N.\thinspace{}M.},
    TITLE = {Higher congruences between modular forms},
  JOURNAL = {Ann. of Math. (2)},
   VOLUME = {101},
     YEAR = {1975},
    PAGES = {332--367},
  MRCLASS = {10D05 (14K15)},
 MRNUMBER = {54 #5120},
   MRREVR = {Neal Koblitz},
}

@inproceedings {katz:antwerp350,
   AUTHOR = {Katz, N.\thinspace{}M.},
    TITLE = {$p$-adic properties of modular schemes and modular forms},
BOOKTITLE = {Modular functions of one variable, III (Proc. Internat. Summer
             School, Univ. Antwerp, Antwerp, 1972)},
    PAGES = {69--190. Lecture Notes in Mathematics, Vol. 350},
PUBLISHER = {Springer},
  ADDRESS = {Berlin},
     YEAR = {1973},
}

@inproceedings {KATZBONN,
   AUTHOR = {Katz, N.\thinspace{}M.},
    TITLE = {A result on modular forms in characteristic $p$},
BOOKTITLE = {Modular functions of one variable, V (Proc. Second Internat.
             Conf., Univ. Bonn, Bonn, 1976)},
    PAGES = {53--61. Lecture Notes in Math., Vol. 601},
PUBLISHER = {Springer},
  ADDRESS = {Berlin},
     YEAR = {1977}
}




@article {pizer:alg,
   AUTHOR = {Pizer, A.},
    TITLE = {An algorithm for computing modular forms on 
             \protect{$\Gamma\sb{0}({N})$}},
  JOURNAL = {J. Algebra},
 FJOURNAL = {Journal of Algebra},
   VOLUME = {64},
     YEAR = {1980},
   NUMBER = {2},
    PAGES = {340--390},
     ISSN = {0021-8693},
    CODEN = {JALGA4},
}

@article {pizer:arithmetic,
   AUTHOR = {Pizer, A.},
    TITLE = {On the arithmetic of quaternion algebras},
  JOURNAL = {Acta Arith.},
   VOLUME = {31},
     YEAR = {1976},
   NUMBER = {1},
    PAGES = {61--89},
}

@article {pizer:arithmetictwo,
   AUTHOR = {Pizer, A.},
    TITLE = {On the arithmetic of quaternion algebras. \protect{II}},
  JOURNAL = {J. Math. Soc. Japan},
   VOLUME = {28},
     YEAR = {1976},
   NUMBER = {4},
    PAGES = {676--688},
}


@article {pizer:rep,
   AUTHOR = {Pizer, A.},
    TITLE = {The representability of modular forms by theta series},
  JOURNAL = {J. Math. Soc. Japan},
   VOLUME = {28},
     YEAR = {1976},
   NUMBER = {4},
    PAGES = {689--698},
}

@book {slnm601,
    TITLE = {Modular functions of one variable. \protect{V}},
BOOKTITLE = {Proceedings of the Second International Conference, held at the
             University of Bonn, Bonn, July 2--14, 1976},
     NOTE = {Edited by J-P. Serre and D. B. Zagier,
             Lecture Notes in Mathematics, Vol. 601},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {1977},
    PAGES = {i+294},
}


@article {mestre-oesterle:crelle,
   AUTHOR = {Mestre, J.-F. and Oesterl{\'e}, J.},
    TITLE = {Courbes de {W}eil semi-stables de discriminant une puissance
             \protect{$m$}-i\`eme},
  JOURNAL = {J. Reine Angew. Math.},
 FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik},
   VOLUME = {400},
     YEAR = {1989},
    PAGES = {173--184},
     ISSN = {0075-4102},
    CODEN = {JRMAA8},
  MRCLASS = {11G18 (11F70 11G05 14G25 14K07)},
 MRNUMBER = {90g:11078},
   MRREVR = {Noriko Yui},
}

@article{ribet:mestreletter,
   author = {Ribet, K.\thinspace{}A.},
   title = {Letter to \protect{M}estre},
   year  = {November, 1987}
}


@proceedings {MR88c:14001,
    TITLE = {Current trends in arithmetical algebraic geometry},
BOOKTITLE = {Proceedings of the AMS-IMS-SIAM joint summer research
             conference held at Humboldt State University, Arcata, Calif.,
             August 18--24, 1985},
   EDITOR = {Ribet, Kenneth A.},
PUBLISHER = {American Mathematical Society},
  ADDRESS = {Providence, R.I.},
     YEAR = {1987},
    PAGES = {x+293},
     ISBN = {0-8218-5070-1},
}

@incollection {SERRE:ARCATA,
   AUTHOR = {Serre, J-P.},
    TITLE = {Lettre \`a {J}.-{F}. {M}estre},
BOOKTITLE = {Current trends in arithmetical algebraic geometry (Arcata,
             Calif., 1985)},
    PAGES = {263--268},
PUBLISHER = {Amer. Math. Soc.},
  ADDRESS = {Providence, RI},
     YEAR = {1987},
}

@article{ribet:lowering,
  author={Ribet, K.\thinspace{}A.},
  title = {Lowering the levels of modular representations 
       without multiplicity one},
  journal={International Mathematics Research Notices},
  year={1991},
  pages={15--19}
}

@article {ribet:modreps,
   AUTHOR = {Ribet, K.\thinspace{}A.},
    TITLE = {On modular representations of 
             \protect{${\rm {G}al}(\overline{\bf{Q}}/{\bf {Q}})$} 
             arising from modular forms},
  JOURNAL = {Invent. Math.},
 FJOURNAL = {Inventiones Mathematicae},
   VOLUME = {100},
     YEAR = {1990},
   NUMBER = {2},
    PAGES = {431--476},
     ISSN = {0020-9910},
    CODEN = {INVMBH},
}



@incollection {ribet:report,
   AUTHOR = {Ribet, K.\thinspace{}A.},
    TITLE = {Report on mod \protect{$\ell$} representations of 
               \protect{${\rm {G}al}(\overline{\bf{Q}}/{\bf {Q}})$}},
BOOKTITLE = {Motives (Seattle, WA, 1991)},
    PAGES = {639--676},
PUBLISHER = {Amer. Math. Soc.},
  ADDRESS = {Providence, RI},
     YEAR = {1994},
}


@book {schilling,
    TITLE = {Arithmetical algebraic geometry. (\protect{P}roceedings of a
             \protect{C}onference held at \protect{P}urdue 
             \protect{U}niversity, \protect{D}ecember 5--7,
             1963)},
   EDITOR = {Schilling, O.\thinspace{}F.\thinspace{}G.},
PUBLISHER = {Harper \& Row Publishers},
  ADDRESS = {New York},
     YEAR = {1965},
    PAGES = {vii+200},
}

@article{ribet:toulouse,
    author={Ribet, K.\thinspace{}A.},
    TITLE = {From the \protect{T}aniyama-\protect{S}himura 
             conjecture to \protect{F}ermat's last theorem},
  JOURNAL = {Ann. Fac. Sci. Toulouse Math. (5)},
 FJOURNAL = {Toulouse. Facult\'e des Sciences. Annales. Math\'ematiques.
             S\'erie 5},
   VOLUME = {11},
     YEAR = {1990},
   NUMBER = {1},
    PAGES = {116--139},
     ISSN = {0240-2955},
}

@inproceedings{HPF,
   AUTHOR = {Swinnerton-Dyer, H.\thinspace{}P.\thinspace{}F.},
    TITLE = {On $\ell$-adic representations and congruences for coefficients of
             modular forms},
BOOKTITLE = {Proceedings of the International Summer School, University of
             Antwerp, RUCA, July 17--August 3, 1972},
    PAGES = {1--55. Lecture Notes in Math., Vol. 350},
PUBLISHER = {Springer},
  ADDRESS = {Berlin},
     YEAR = {1973},
}

@article{SERRETAU,
   author = {Serre, J-P.},
   title  = {Une \protect{interpr\'etation} 
     des congruences relatives \protect{\`a}
     la fonction \protect{$\tau$} de {R}amanujan},
   journal = {\protect{S\'eminaire Delange-Pisot-Poitou}},
   year    = {1967--68},
   volume  = {\protect{$n^o$} 14}
}

@incollection {gruenberg,
   AUTHOR = {Gruenberg, K.},
    TITLE = {Profinite groups},
BOOKTITLE = {Algebraic Number Theory (Proc. Instructional Conf., Brighton,
             1965)},
    PAGES = {116--127},
PUBLISHER = {Thompson, Washington, D.C.},
     YEAR = {1967},
}

@book {MR35:6500,
    TITLE = {Algebraic number theory},
BOOKTITLE = {Proceedings of an instructional conference organized by the
             London Mathematical Society (a NATO Advanced Study Institute)
             with the support of the Inter national Mathematical Union.
             Edited by J. W. S. Cassels and A. Fr\"ohlich},
PUBLISHER = {Academic Press},
  ADDRESS = {London},
     YEAR = {1967},
    PAGES = {xviii+366},
}

@book {serre:gc,
   AUTHOR = {Serre, J-P.},
    TITLE = {Galois cohomology},
     NOTE = {Translated from the French by Patrick Ion and revised by the
             author},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {1997},
    PAGES = {x+210},
     ISBN = {3-540-61990-9},
}
   
@book {serre:ladic,
   AUTHOR = {Serre, J-P.},
    TITLE = {Abelian \protect{$\ell$}-adic representations and elliptic curves},
     NOTE = {With the collaboration of Willem Kuyk and John Labute,
             Revised reprint of the 1968 original},
PUBLISHER = {A\thinspace{}K Peters Ltd.},
  ADDRESS = {Wellesley, MA},
     YEAR = {1998},
    PAGES = {199},
     ISBN = {1-56881-077-6},
}


@book {serre:linear,
   AUTHOR = {Serre, J-P.},
    TITLE = {Linear representations of finite groups},
     NOTE = {Translated from the second French edition by Leonard L. Scott,
             Graduate Texts in Mathematics, Vol. 42},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {New York},
     YEAR = {1977},
    PAGES = {x+170},
     ISBN = {0-387-90190-6},
}


@incollection {serre:local,
   AUTHOR = {Serre, J-P.},
    TITLE = {Local class field theory},
BOOKTITLE = {Algebraic Number Theory (Proc. Instructional Conf., Brighton,
             1965)},
    PAGES = {128--161},
PUBLISHER = {Thompson, Washington, D.C.},
     YEAR = {1967},
}

@book {serre:alggroups,
   AUTHOR = {Serre, J-P.},
    TITLE = {Algebraic groups and class fields},
     NOTE = {Translated from the French},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {New York},
     YEAR = {1988},
    PAGES = {x+207},
     ISBN = {0-387-96648-X},
}

@book {serre:arithmetic,
   AUTHOR = {Serre, J-P.},
    TITLE = {A \protect{C}ourse in \protect{A}rithmetic},
     NOTE = {Translated from the French,
             Graduate Texts in Mathematics, No. 7},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {New York},
     YEAR = {1973},
    PAGES = {viii+115},
}


@book {serre:localfields,
   AUTHOR = {Serre, J-P.},
    TITLE = {Local fields},
     NOTE = {Translated from the French by Marvin Jay Greenberg},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {New York},
     YEAR = {1979},
    PAGES = {viii+241},
     ISBN = {0-387-90424-7},
}

@article{serre:propgal, 
   AUTHOR = {Serre, J-P.},
    TITLE = {Propri\'et\'es galoisiennes des points d'ordre fini des courbes
             elliptiques},
  JOURNAL = {Invent. Math.},
   VOLUME = {15},
     YEAR = {1972},
   NUMBER = {4},
    PAGES = {259--331},
}

@article{serre:propres,
   author={Serre, J-P.},
   title={Valeurs propres des \protect{op\'{e}rateurs} de
          \protect{Hecke} modulo \protect{$\ell$}},
   journal = {\protect{Ast\'{e}risque}},
   volume = {24--25},
   year   = {1975},
   pages  = {109--117}
}

@article {serre:conjectures,
   AUTHOR = {Serre, J-P.},
    TITLE = {Sur les repr\'esentations modulaires de degr\'e \protect{$2$} 
             de \protect{${\rm{G}al}(\overline{\bf {Q}}/{\bf {Q}})$}},
  JOURNAL = {Duke Math. J.},
 FJOURNAL = {Duke Mathematical Journal},
   VOLUME = {54},
     YEAR = {1987},
   NUMBER = {1},
    PAGES = {179--230},
     ISSN = {0012-7094},
    CODEN = {DUMJAO},
}


@article {serre-tate,
   AUTHOR = {Serre, J-P. and Tate, J.\thinspace{}T.},
    TITLE = {Good reduction of abelian varieties},
  JOURNAL = {Ann. of Math. (2)},
   VOLUME = {88},
     YEAR = {1968},
    PAGES = {492--517},
}

@article{shimura:factors,
    AUTHOR = {Shimura, G.},
    TITLE={On the factors of the jacobian variety of a modular function field},
    journal={J. Math. Soc. Japan},
    volume={25},
    number={3},
    year={1973},
    pages={523--544},
}

@article{shimura:onperiods,
    author={Shimura, G.},
    title={On the periods of modular forms},
    journal={Math. Ann.},
    volume={229},
    pages={211--221},
    year={1977}
}

@article {shimura:surles,
   AUTHOR = {Shimura, G.},
    TITLE = {Sur les \protect{int\'egrales} \protect{attach\'ees} 
             aux formes automorphes},
  JOURNAL = {J. Math. Soc. Japan},
   VOLUME = {11},
     YEAR = {1959},
    PAGES = {291--311},
}

@book {silverman:aec,
   AUTHOR = {Silverman, J.\thinspace{}H.},
    TITLE = {The arithmetic of elliptic curves},
     NOTE = {Corrected reprint of the 1986 original},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {New York},
     YEAR = {1992},
    PAGES = {xii+400},
     ISBN = {0-387-96203-4},
}

@book {silverman:aec2,
   AUTHOR = {Silverman, J.\thinspace{}H.},
    TITLE = {Advanced topics in the arithmetic of elliptic curves},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {New York},
     YEAR = {1994},
    PAGES = {xiv+525},
     ISBN = {0-387-94328-5},
}

@article{stein:compgroup,
    author = "Conrad, B. and Stein, W.\thinspace{}A.",
    title = {Component {G}roups of {P}urely {T}oric {Q}uotients},
    journal = {to appear in Math Research Letters},
    year = {2002}
}

@article{stein:congruence,
    author = "Stein, W.\thinspace{}A.",
    title  = {Congruences between modular forms},
    journal = {Notes},
    year = {1999}
}

@article{generatinghecke,
    author = "Agashe, A. and Stein, W.\thinspace{}A.",
    title  = {Generating the \protect{H}ecke algebra},
    journal = {preprint},
    year = {1999}
}

@article{stein:hecke,
    author = "Stein, W.\thinspace{}A.",
    title  = {\protect{{\tt HECKE}: The} modular symbols calculator},
    journal = {Software (available online)},
    year = {1999}
}

@article{stein:database,
    author = "Stein, W.\thinspace{}A.",
    title  = {The modular forms database,\hfill\\
      \protect{\sf http://modular.fas.harvard.edu}}
}


@article{stein-verrill:periods,
    author = "Stein, W.\thinspace{}A. and Verrill, H.\thinspace{}A.",
    title = {Computing period lattices associated to newforms},
    journal = {In preparation},
    year = {2000}
}

@article{stein-verrill:transportable,
    author = "Stein, W.\thinspace{}A. and Verrill, H.\thinspace{}A.",
    title = {Cuspidal modular symbols are transportable},
   JOURNAL = {LMS J. Comput. Math.},
  FJOURNAL = {LMS Journal of Computation and Mathematics},
    VOLUME = {4},
      YEAR = {2001},
     PAGES = {170--181 (electronic)},
      ISSN = {1461-1570},
   MRCLASS = {11F67},
  MRNUMBER = {1 901 355}
}

@article{stein:phd,
    author="Stein, W.\thinspace{}A.",
    title={Explicit approaches to modular abelian varieties},
    journal = {Ph.D. thesis, University of California, Berkeley},
    year={2000}
}

@article{klenke:phd,
    author="Klenke, T.",
    title={Modular {V}arieties and {V}isibility},
    journal = {Ph.D. thesis, Harvard University},
    year={2001}
}

@article{stein:modsyms,
    author = "Stein, W.\thinspace{}A.",
    title = {An introduction to computing modular forms using modular symbols},
    journal = {to appear in an MSRI Proceedings},
    year = {2002}
}


@article{agashe:phd,
    author="Agashe, A.",
    title={The {B}irch and {S}winnerton-{D}yer formula for modular 
           abelian varieties of analytic rank~$0$},
    journal = {Ph.D. thesis, University of California, Berkeley},
    year={2000}
}

@article{tate:nonexistence,
    author={Tate, J.\thinspace{}T.},
    title={The non-existence of certain \protect{Galois} extensions
    of \protect{$\Q$} unramified outside \protect{$2$}},
    journal={Contemporary Math.},
    volume={174},
    year={1994},
    pages={153--156}
}

@incollection {tate:global,
   AUTHOR = {Tate, J.\thinspace{}T.},
    TITLE = {Global class field theory},
BOOKTITLE = {Algebraic Number Theory (Proc. Instructional Conf., Brighton,
             1965)},
    PAGES = {162--203},
PUBLISHER = {Thompson, Washington, D.C.},
     YEAR = {1967},
}


@Comment {should be V\'{e}lu but this causes problems.}
@inproceedings {velu:groupes,
   AUTHOR = {V\'{e}lu, J.},     
    TITLE = {Groupes de \protect{G}alois 
             attach\'es aux points d'ordre fini des
             courbes elliptiques sur un corps de 
             nombres, d'apr\`es \protect{J}.
             \protect{P}. \protect{S}erre},
BOOKTITLE = {S\'eminaire de Th\'eorie des Nombres, 1971--1972 (Univ.
             Bordeaux I, Talence), Exp. No. 30},
    PAGES = {12},
PUBLISHER = {Lab. Th\'eorie des Nombres, Centre Nat. Recherche Sci.,
             Talence},
     YEAR = {1972},
}



@book {MR52:8007,
    TITLE = {S\'eminaire de {T}h\'eorie des {N}ombres. 1971--1972},
     NOTE = {Tenu \`a l'Universit\'e de Bordeaux I, Talence, ann\'ee
             universitaire 1971--1972},
PUBLISHER = {Laboratoire de Th\'eorie des Nombres, Centre National de
             Recherche Scientifique, Talence},
     YEAR = {1972},
    PAGES = {224 pp. (not consecutively paged)},
}

@inproceedings{diamond:refined,
   AUTHOR = {Diamond, F.},
    TITLE = {The refined conjecture of \protect{S}erre},
BOOKTITLE = {Elliptic curves, modular forms, \& 
             \protect{F}ermat's last theorem (\protect{H}ong
             \protect{K}ong, 1993)},
    PAGES = {22--37},
PUBLISHER = {Internat. Press},
  ADDRESS = {Cambridge, MA},
     YEAR = {1995},
}


@book {MR96f:11004,
    TITLE = {Seminar on {F}ermat's {L}ast {T}heorem},
   EDITOR = {Murty, V. Kumar},
     NOTE = {Papers from the seminar held at the Fields Institute for
             Research in Mathematical Sciences, Toronto, Ontario,
             1993--1994},
PUBLISHER = {Published by the American Mathematical Society, Providence, RI},
     YEAR = {1995},
    PAGES = {x+265},
     ISBN = {0-8218-0313-1},
  MRCLASS = {11-06 (11D41 11G05 11G18)},
 MRNUMBER = {96f:11004},
}

@incollection{diamond-im,
   AUTHOR = {Diamond, F. and Im, J.},
    TITLE = {Modular forms and modular curves},
BOOKTITLE = {Seminar on {F}ermat's {L}ast {T}heorem},
    PAGES = {39--133},
ppPUBLISHER = {Amer. Math. Soc.},
  ADDRESS = {Providence, RI},
     YEAR = {1995},
}



@book {murty-murty,
   AUTHOR = {Murty, M.\thinspace{}R. and Murty, V.\thinspace{}K.},
    TITLE = {Non-vanishing of ${L}$-functions and applications},
PUBLISHER = {Birkh\"auser Verlag},
  ADDRESS = {Basel},
     YEAR = {1997},
    PAGES = {xii+196},
     ISBN = {3-7643-5801-7},
}

@proceedings{boston,
    TITLE = {Modular forms and \protect{F}ermat's last theorem (Boston,MA, 1995)},
   EDITOR = {Cornell, G. and Silverman, J.\thinspace{}H. and Stevens, G.},
     NOTE = {Papers from the Instructional Conference on Number Theory and
             Arithmetic Geometry held at Boston University, Boston, MA,
             August 9--18, 1995},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {New York},
     YEAR = {1997},
    PAGES = {xx+582},
     ISBN = {0-387-94609-8},
}

@inproceedings{DELIGNE,
   author = {Deligne, P.},
    title={Formes modulaires et \protect{repr\'{e}sentations $\ell$-adiques.}},
     NOTE = {Lecture Notes in Mathematics, Vol. 179},
PUBLISHER = {Springer-Verlag},
  booktitle = {\protect{S\'{e}m.} Bourbaki no. 355, 1968/69},
  ADDRESS = {Berlin and New York},
  year = {1971},
  pages = {139--172}
}

@book{MR,
    TITLE = {\protect{S\'{e}m.} Bourbaki no. 355, 1968/69},
     NOTE = {Lecture Notes in Mathematics, Vol. 179},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin and New York},
  YEAR    = {1971}
}

@book {MR48:8389,
    TITLE = {Modular functions of one variable. {I}{I}},
BOOKTITLE = {Proceedings of the International Summer 
             School, University of
             Antwerp, RUCA, July 17--August 3, 1972},
   EDITOR = {Deligne, P. and Kuyk, W.},
     NOTE = {Lecture Notes in Mathematics, Vol. 349},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {1973},
    PAGES = {iv+598},
}

@book {MR48:2080,
    TITLE = {Modular functions of one variable. {I}{I}{I}},
BOOKTITLE = {Proceedings of the International Summer School, University of
             Antwerp, RUCA, July 17--August 3, 1972},
   EDITOR = {Kuyk, W. and Serre, J-P.},
     NOTE = {Lecture Notes in Mathematics, Vol. 350},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {1973},
    PAGES = {iv+350},
}

@article{ntl,
    title = {\protect{NTL: Number} theory library},
   author = {Shoup, V.},
}

@article{lidia,
    title = {\protect{LiDIA: C++} number theory library},
   author = {Buchmann, J.}
}

@article{cremona-luiz,
    title = {\protect{C++} matrix classes},
   author = {Cremona, J.\thinspace{}E. and Luiz F.}
}

@book {freyetal,
    TITLE = {On {A}rtin's conjecture for odd 2-dimensional representations},
BOOKTITLE = {On {A}rtin's conjecture for odd 2-dimensional representations},
   EDITOR = {Frey, G.},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {1994},
    PAGES = {viii+148},
     ISBN = {3-540-58387-4},
}

@article{winnie:newforms,
   AUTHOR = {Li, W-C.},
    TITLE = {Newforms and functional equations},
  JOURNAL = {Math. Ann.},
   VOLUME = {212},
     YEAR = {1975},
    PAGES = {285--315},
}


@inproceedings {casselman,
   AUTHOR = {Casselman, W.},
    TITLE = {On representations of 
   \protect{${\rm {G}{L}}\sb{2}$} and the arithmetic
             of modular curves},
BOOKTITLE = {Modular functions of one variable, II (Proc. Internat. Summer
             School, Univ. Antwerp, Antwerp, 1972)},
    PAGES = {107--141. Lecture Notes in Math., Vol. 349},
PUBLISHER = {Springer},
  ADDRESS = {Berlin},
     YEAR = {1973},
}


@proceedings {cassels-frohlich,
    TITLE = {Algebraic number theory},
BOOKTITLE = {Proceedings of the instructional conference held at the
             University of Sussex, Brighton, September 1--17, 1965},
   EDITOR = {Cassels, J.\thinspace{}W.\thinspace{}S. and 
     \protect{Fr{\"o}hlich}, A.},
     NOTE = {Reprint of the 1967 original},
PUBLISHER = {Academic Press Inc. [Harcourt Brace Jovanovich Publishers]},
  ADDRESS = {London},
     YEAR = {1986},
    PAGES = {xviii+366},
     ISBN = {0-12-163251-2},
}


@inproceedings {waldspurger:corr,
   AUTHOR = {Waldspurger, J.-L.},
    TITLE = {Correspondances de {S}himura},
BOOKTITLE = {Proceedings of the International Congress of Mathematicians,
             Vol.\ 1, 2 (Warsaw, 1983)},
    PAGES = {525--531},
PUBLISHER = {PWN},
  ADDRESS = {Warsaw},
     YEAR = {1984},
}

@proceedings {MR86g:00010,
    TITLE = {Proceedings of the international congress of mathematicians.
             {V}ol. 1, 2},
   EDITOR = {Ciesielski, Zbigniew and Olech, Czes{\l}aw},
     NOTE = {Held in Warsaw, August 16--24, 1983},
PUBLISHER = {PWN---Polish Scientific Publishers},
  ADDRESS = {Warsaw},
     YEAR = {1984},
    PAGES = {lxii+1730},
     ISBN = {83-01-05523-5},
}

@article {schur:arith,
  author={Schur, I.},
  title = {Arithmetische {U}ntersuchungen \"uber endliche {G}ruppen
linearer {S}ubstitutionen},
  journal={Sitz. Pr. Akad. Wiss.},
  year = {1906},
  pages = {164--184},
  note = {Gesam. Abhl., {\bf I}, 177--197, Springer-Verlag,
      Berlin-Heidelberg-New York-Tokyo, 1973}
}  

@article {waldspurger:comp1,
   AUTHOR = {Waldspurger, J.-L.},
    TITLE = {Quelques propri\'et\'es arithm\'etiques de certaines formes
             automorphes sur \protect{${\rm {G}{L}}(2)$}},
  JOURNAL = {Compositio Math.},
 FJOURNAL = {Compositio Mathematica},
   VOLUME = {54},
     YEAR = {1985},
   NUMBER = {2},
    PAGES = {121--171},
     ISSN = {0010-437X},
    CODEN = {CMPMAF},
  MRCLASS = {11F70 (22E55)},
 MRNUMBER = {87g:11061a},
   MRREVR = {Stephen Gelbart},
}

@article {waldspurger:comp2,
   AUTHOR = {Waldspurger, J.-L.},
    TITLE = {Sur les valeurs de certaines fonctions \protect{${L}$} automorphes en
             leur centre de sym\'etrie},
  JOURNAL = {Compositio Math.},
 FJOURNAL = {Compositio Mathematica},
   VOLUME = {54},
     YEAR = {1985},
   NUMBER = {2},
    PAGES = {173--242},
     ISSN = {0010-437X},
    CODEN = {CMPMAF},
  MRCLASS = {11F70 (11F67 22E55)},
 MRNUMBER = {87g:11061b},
   MRREVR = {Stephen Gelbart},
}


@article {khare:manu,
   AUTHOR = {Khare, C.},
    TITLE = {Multiplicities of mod $p$ {G}alois representations},
  JOURNAL = {Manuscripta Math.},
 FJOURNAL = {Manuscripta Mathematica},
   VOLUME = {95},
     YEAR = {1998},
   NUMBER = {2},
    PAGES = {181--188},
     ISSN = {0025-2611},
    CODEN = {MSMHB2},
  MRCLASS = {11F80 (11F33 11G18)},
 MRNUMBER = {98m:11046},
   MRREVR = {Ian Kiming},
}



@book {greenberg-harper,
   AUTHOR = {Greenberg, M.\thinspace{}J. and Harper, J.\thinspace{}R.},
    TITLE = {Algebraic topology},
     NOTE = {A first course},
PUBLISHER = {Benjamin/Cummings Publishing Co. Inc. Advanced Book Program},
  ADDRESS = {Reading, Mass.},
     YEAR = {1981},
    PAGES = {xi+311 pp. (loose errata)},
     ISBN = {0-8053-3558-7; 0-8053-3557-9},
  MRCLASS = {55-01},
 MRNUMBER = {83b:55001},
   MRREVR = {J. P. May},
}

@inproceedings {wada1,
   AUTHOR = {Wada, H.},
    TITLE = {Tables of {H}ecke operations. {I}},
BOOKTITLE = {Seminar on {M}odern {M}ethods in {N}umber {T}heory},
    PAGES = {10},
PUBLISHER = {Inst. Statist. Math.},
  ADDRESS = {Tokyo},
     YEAR = {1971},
  MRCLASS = {10D05},
 MRNUMBER = {52 #282},
   MRREVR = {Kuang-yen Shih},
}

@book {MR50:4458,
    TITLE = {Seminar on {M}odern {M}ethods in {N}umber {T}heory},
     NOTE = {Held at the Institute of Statistical Mathematics, Tokyo, August
             30--September 4, 1971},
PUBLISHER = {Institute of Statistical Mathematics},
  ADDRESS = {Tokyo},
     YEAR = {1971},
    PAGES = {iii+291 pp. (not consecutively paged)},
  MRCLASS = {10-06},
 MRNUMBER = {50 #4458},
}

@article {coleman:banach,
   AUTHOR = {Coleman, R.\thinspace{}F.},
    TITLE = {$p$-adic {B}anach spaces and families of modular forms},
  JOURNAL = {Invent. Math.},
 FJOURNAL = {Inventiones Mathematicae},
   VOLUME = {127},
     YEAR = {1997},
   NUMBER = {3},
    PAGES = {417--479},
     ISSN = {0020-9910},
    CODEN = {INVMBH},
  MRCLASS = {11F33 (11F67 11F85 11G07 14E30)},
 MRNUMBER = {98b:11047},
   MRREVR = {Alexey A. Panchishkin},
}

@book {bgr,
   AUTHOR = {Bosch, S. and G{\"u}ntzer, U. and Remmert, R.},
    TITLE = {Non-{A}rchimedean analysis: A systematic approach to rigid analytic geometry},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {1984},
    PAGES = {xii+436},
     ISBN = {3-540-12546-9},
  MRCLASS = {32K10 (30G05 46P05)},
 MRNUMBER = {86b:32031},
   MRREVR = {W. Bartenwerfer},
}

@article{coleman:classical,
    AUTHOR={Coleman, R.\thinspace{}F.},
    TITLE = {Classical and overconvergent modular forms},
  JOURNAL = {Invent. Math.},
 FJOURNAL = {Inventiones Mathematicae},
   VOLUME = {124},
     YEAR = {1996},
   NUMBER = {1-3},
    PAGES = {215--241},
     ISSN = {0020-9910},
    CODEN = {INVMBH},
  MRCLASS = {11F85 (14G20)},
 MRNUMBER = {97d:11090a},
   MRREVR = {Fernando Q. Gouv\^ea},
}


@article{coleman:classical_higher,
    AUTHOR={Coleman, R.\thinspace{}F.},
    TITLE = {Classical and overconvergent modular forms of higher level},
  JOURNAL = {J. Th\'eor. Nombres Bordeaux},
 FJOURNAL = {Journal de Th\'eorie des Nombres de Bordeaux},
   VOLUME = {9},
     YEAR = {1997},
   NUMBER = {2},
    PAGES = {395--403},
     ISSN = {1246-7405},
  MRCLASS = {11F85 (11F11)},
 MRNUMBER = {99g:11071},
   MRREVR = {Conjeeveram S. Rajan}
}


@incollection {jochnowitz:conjecture,
   AUTHOR = {Jochnowitz, N.},
    TITLE = {A $p$-adic conjecture about derivatives of ${L}$-series
             attached to modular forms},
BOOKTITLE = {$p$-adic monodromy and the {B}irch and {S}winnerton-{D}yer
             conjecture},
    PAGES = {239--263},
PUBLISHER = {Amer. Math. Soc.},
  ADDRESS = {Providence, RI},
     YEAR = {1994},
  MRCLASS = {11F33 (11F67 11F85 11G40)},
 MRNUMBER = {95g:11037},
   MRREVR = {Andrea Mori},
}

@book {MR94m:11006,
    TITLE = {$p$-adic monodromy and the {B}irch and {S}winnerton-{D}yer
             conjecture},
   EDITOR = {Mazur, Barry and Stevens, Glenn},
     NOTE = {Papers from the workshop held at Boston University, Boston,
             Massachusetts, August 12--16, 1991},
PUBLISHER = {American Mathematical Society},
  ADDRESS = {Providence, RI},
     YEAR = {1994},
    PAGES = {xiv+315},
     ISBN = {0-8218-5180-2},
  MRCLASS = {11-06 (11G40)},
 MRNUMBER = {94m:11006},
}

@article{guerzhoy:kummer,
   title  = {Searching for {K}ummer congruences in an infinite
             slope family},
   author = {Guerzhoy, P.},
   year   = {2000},
   journal = {Preprint}
}

@article {serre:travauxwiles,
    AUTHOR = {Serre, J-P.},
     TITLE = {Travaux de {W}iles (et {T}aylor, $\ldots$). {I}},
      NOTE = {S\'eminaire Bourbaki, Vol.\ 1994/95},
   JOURNAL = {Ast\'erisque},
  FJOURNAL = {Ast\'erisque},
    NUMBER = {237},
      YEAR = {1996},
     PAGES = {Exp.\ No.\ 803, 5, 319--332},
      ISSN = {0303-1179},
   MRCLASS = {11G05 (11D41 11F80 11F85 11G18)},
  MRNUMBER = {97m:11076},
MRREVIEWER = {Alexey A. Panchishkin},
}



@incollection {mccallum:kolyvagin,
    AUTHOR = {McCallum, W.\thinspace{}G.},
     TITLE = {Kolyvagin's work on {S}hafarevich-{T}ate groups},
 BOOKTITLE = {$L$-functions and arithmetic (Durham, 1989)},
     PAGES = {295--316},
 PUBLISHER = {Cambridge Univ. Press},
   ADDRESS = {Cambridge},
      YEAR = {1991},
   MRCLASS = {11G40 (11G05 14G10)},
  MRNUMBER = {92m:11062},
MRREVIEWER = {John Jones},
}


@incollection {murty:congruence,
   AUTHOR = {Murty, M.\thinspace{}R.},
    TITLE = {Bounds for congruence primes},
BOOKTITLE = {Automorphic forms, automorphic representations, and arithmetic
             (Fort Worth, TX, 1996)},
    PAGES = {177--192},
PUBLISHER = {Amer. Math. Soc.},
  ADDRESS = {Providence, RI},
     YEAR = {1999},
  MRCLASS = {11F66 (11G05)},
 MRNUMBER = {2000g:11038},
   MRREVR = {Alexey A. Panchishkin},
}

@proceedings {MR2000c:11002,
    TITLE = {Automorphic forms, automorphic representations, and arithmetic},
BOOKTITLE = {Proceedings of the NSF-CBMS Regional Conference in Mathematics
             on Euler Products and Eisenstein Series held at Texas Christian
             University, Fort Worth, TX, May 20--24, 1996},
   EDITOR = {Doran, Robert S. and Dou, Ze-Li and Gilbert, George T.},
PUBLISHER = {American Mathematical Society},
  ADDRESS = {Providence, RI},
     YEAR = {1999},
    PAGES = {xii+278},
     ISBN = {0-8218-0659-9},
  MRCLASS = {11-06 (11Fxx)},
 MRNUMBER = {2000c:11002},
}

@article {brumer-mcguinness,
    AUTHOR = {Brumer, A. and McGuinness, O.},
     TITLE = {The behavior of the {M}ordell-{W}eil group of elliptic curves},
   JOURNAL = {Bull. Amer. Math. Soc. (N.S.)},
  FJOURNAL = {American Mathematical Society. Bulletin. New Series},
    VOLUME = {23},
      YEAR = {1990},
    NUMBER = {2},
     PAGES = {375--382},
      ISSN = {0273-0979},
     CODEN = {BAMOAD},
   MRCLASS = {11G40 (11-04 11G05)},
  MRNUMBER = {91b:11076},
MRREVIEWER = {Kenneth Kramer},
   note    = {\protect{\sf http://shimura.math.berkeley.edu/\~{ }oisin/}}
}

@article {buhler-gross,
    AUTHOR = {Buhler, J.\thinspace{}P. and Gross, B.\thinspace{}H.},
     TITLE = {Arithmetic on elliptic curves with complex multiplication.
              {I}{I}},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {79},
      YEAR = {1985},
    NUMBER = {1},
     PAGES = {11--29},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {11G40 (11G05 14K22)},
  MRNUMBER = {86j:11066},
MRREVIEWER = {Kenneth Kramer},
}





@book {lang:nt3,
    AUTHOR = {Lang, S.},
     TITLE = {Number theory. {I}{I}{I}},
      NOTE = {Diophantine geometry},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1991},
     PAGES = {xiv+296},
      ISBN = {3-540-53004-5},
   MRCLASS = {11Gxx (14Gxx)},
  MRNUMBER = {93a:11048},
MRREVIEWER = {Joseph H. Silverman},
}

@article {agashe-stein:schoof-appendix,
    AUTHOR = {Agashe, A. and Stein, W.\thinspace{}A.},
     TITLE = {{\em Appendix to {J}oan-{C}. {L}ario and 
{R}en\'e {S}choof:} {S}ome computations with {H}ecke 
rings and deformation rings},
   JOURNAL = {to appear in Exp. Math.}
}

@incollection {edixhoven:manin,
    AUTHOR = {Edixhoven, B.},
     TITLE = {On the {M}anin constants of modular elliptic curves},
 BOOKTITLE = {Arithmetic algebraic geometry (Texel, 1989)},
     PAGES = {25--39},
 PUBLISHER = {Birkh\"auser Boston},
   ADDRESS = {Boston, MA},
      YEAR = {1991},
   MRCLASS = {11G05 (14G25)},
  MRNUMBER = {92a:11066},
MRREVIEWER = {Philippe Satg{\'e}},
}

@incollection {tate:antwerpiv,
    AUTHOR = {Tate, J.},
     TITLE = {Algorithm for determining the type of a singular fiber in an
              elliptic pencil},
 BOOKTITLE = {Modular functions of one variable, IV (Proc. Internat. Summer
              School, Univ. Antwerp, Antwerp, 1972)},
     PAGES = {33--52. Lecture Notes in Math., Vol. 476},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {1975},
   MRCLASS = {14G25 (14K15)},
  MRNUMBER = {52 \#13850},
MRREVIEWER = {J. S. Milne},
}

@article {ega4_1,
    AUTHOR = {Grothendieck, A.},
     TITLE = {\'{E}l\'ements de g\'eom\'etrie alg\'ebrique. {I}{V}.
              \'{E}tude locale des sch\'emas et des morphismes de sch\'emas.
              {I}},
   JOURNAL = {Inst. Hautes \'Etudes Sci. Publ. Math.},
    NUMBER = {20},
      YEAR = {1964},
     PAGES = {259},
   MRCLASS = {14.05 (13.10)},
  MRNUMBER = {30 \#3885},
MRREVIEWER = {H. Hironaka},
}


@article {ega4_2,
    AUTHOR = {Grothendieck, A.},
     TITLE = {\'{E}l\'ements de g\'eom\'etrie alg\'ebrique. {I}{V}.
              \'{E}tude locale des sch\'emas et des morphismes de sch\'emas.
              {I}{I}},
   JOURNAL = {Inst. Hautes \'Etudes Sci. Publ. Math.},
    NUMBER = {24},
      YEAR = {1965},
     PAGES = {231},
   MRCLASS = {14.00},
  MRNUMBER = {33 \#7330},
MRREVIEWER = {H. Hironaka},
}


@article {ega4_3,
    AUTHOR = {Grothendieck, A.},
     TITLE = {\'{E}l\'ements de g\'eom\'etrie alg\'ebrique. {I}{V}.
              \'{E}tude locale des sch\'emas et des morphismes de sch\'emas.
              {I}{I}{I}},
   JOURNAL = {Inst. Hautes \'Etudes Sci. Publ. Math.},
    NUMBER = {28},
      YEAR = {1966},
     PAGES = {255},
   MRCLASS = {14.55},
  MRNUMBER = {36 \#178},
MRREVIEWER = {J. P. Murre},
}


@article {ega4_4,
    AUTHOR = {Grothendieck, A.},
     TITLE = {\'{E}l\'ements de g\'eom\'etrie alg\'ebrique. {I}{V}.
              \'{E}tude locale des sch\'emas et des morphismes de sch\'emas
              {I}{V}},
   JOURNAL = {Inst. Hautes \'Etudes Sci. Publ. Math.},
    NUMBER = {32},
      YEAR = {1967},
     PAGES = {361},
   MRCLASS = {14.55},
  MRNUMBER = {39 \#220},
MRREVIEWER = {J. P. Murre},
}


@article {edixhoven:minimal,
    AUTHOR = {Edixhoven, B.},
     TITLE = {Minimal resolution and stable reduction of \protect{${X}\sb 0({N})$}},
   JOURNAL = {Ann. Inst. Fourier (Grenoble)},
  FJOURNAL = {Universit\'e de Grenoble. Annales de l'Institut Fourier},
    VOLUME = {40},
      YEAR = {1990},
    NUMBER = {1},
     PAGES = {31--67},
      ISSN = {0373-0956},
     CODEN = {AIFUA7},
   MRCLASS = {11G18 (14G35)},
  MRNUMBER = {92f:11080},
MRREVIEWER = {Autorreferat},
}


@article {serre:pseudoreflections,
    AUTHOR = {Serre, J-P.},
     TITLE = {Groupes finis d'automorphismes d'anneaux locaux r\'eguliers},
 journal = {Colloque d'Alg\`ebre (Paris, 1967), Exp. 8},
     PAGES = {11},
 PUBLISHER = {Secr\'etariat math\'ematique},
   ADDRESS = {Paris},
      YEAR = {1968},
   MRCLASS = {13.95},
  MRNUMBER = {38 \#3267},
MRREVIEWER = {Y. Nakai},
}

@book {gouvea:slnm,
    AUTHOR = {Gouv\^{e}a, F.\thinspace{}Q.},
     TITLE = {Arithmetic of $p$-adic modular forms},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1988},
     PAGES = {viii+121},
      ISBN = {3-540-18946-7},
   MRCLASS = {11F85 (11F80)},
  MRNUMBER = {91e:11056},
MRREVIEWER = {Alexey A. Panchishkin},
}


@incollection {gouvea-mazur:density,
    AUTHOR = {Gouv\^{e}a, F.\thinspace{}Q. and Mazur, B.},
     TITLE = {On the density of modular representations},
 BOOKTITLE = {Computational perspectives on number theory (Chicago, IL,
              1995)},
     PAGES = {127--142},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {1998},
   MRCLASS = {11F33 (11F80)},
  MRNUMBER = {99a:11056},
MRREVIEWER = {Andrea Mori},
}



@article {mazur:infinite_fern,
    AUTHOR = {Mazur, B.},
     TITLE = {An ``infinite fern'' in the universal deformation space of
              {G}alois representations},
      NOTE = {Journ\'ees Arithm\'etiques (Barcelona, 1995)},
   JOURNAL = {Collect. Math.},
  FJOURNAL = {Universitat de Barcelona. Collectanea Mathematica},
    VOLUME = {48},
      YEAR = {1997},
    NUMBER = {1-2},
     PAGES = {155--193},
      ISSN = {0010-0757},
     CODEN = {COLMBA},
   MRCLASS = {11F33 (11F80)},
  MRNUMBER = {98g:11053},
MRREVIEWER = {Andrea Mori},
}


@book {sga3.1,
    AUTHOR = {Grothendieck, A.},
     TITLE = {Sch\'emas en groupes. {I}: {P}ropri\'et\'es g\'en\'erales des
              sch\'emas en groupes},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1970},
     PAGES = {xv+564},
   MRCLASS = {14.50},
  MRNUMBER = {43 \#223a},
}

@book {sga3.2,
    AUTHOR = {Grothendieck, A.},
     TITLE = {Sch\'emas en groupes. {I}{I}: {G}roupes de type multiplicatif,
              et structure des sch\'emas en groupes g\'en\'eraux},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1962/1964},
     PAGES = {ix+654},
   MRCLASS = {14.50},
  MRNUMBER = {43 \#223b},
}

@book {sga3.3,
    AUTHOR = {Grothendieck, A.},
     TITLE = {Sch\'emas en groupes. {I}{I}{I}: {S}tructure des sch\'emas en
              groupes r\'eductifs},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1962/1964},
     PAGES = {viii+529},
   MRCLASS = {14.50},
  MRNUMBER = {43 \#223c},
}

@book {sga7.2,
     author = {Deligne, P. and Katz, N.},
     TITLE = {Groupes de monodromie en g\'eom\'etrie alg\'ebrique. {I}{I}},
      NOTE = {S\'eminaire de G\'eom\'etrie Alg\'ebrique du Bois-Marie
              1967--1969 (SGA 7 II),
              Dirig\'e par P. Deligne et N. Katz,
              Lecture Notes in Mathematics, Vol. 340},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1973},
     PAGES = {x+438},
   MRCLASS = {14-06},
  MRNUMBER = {50 \#7135},
}



@book {hindry-silverman:diophantine,
    AUTHOR = {Hindry, Marc and Silverman, Joseph H.},
     TITLE = {Diophantine geometry},
      NOTE = {An introduction},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {2000},
     PAGES = {xiv+558},
      ISBN = {0-387-98975-7; 0-387-98981-1},
   MRCLASS = {11Gxx (11-02 11G10 11G30 11G50 14G25)},
  MRNUMBER = {2001e:11058},
MRREVIEWER = {Dino J. Lorenzini},
}




@article {poonen-stoll,
    AUTHOR = {Poonen, B. and Stoll, M.},
     TITLE = {The {C}assels-{T}ate pairing on polarized abelian varieties},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {150},
      YEAR = {1999},
    NUMBER = {3},
     PAGES = {1109--1149},
      ISSN = {0003-486X},
     CODEN = {ANMAAH},
   MRCLASS = {11G10 (11G30 14H40 14K15)},
  MRNUMBER = {2000m:11048},
MRREVIEWER = {Tam{\'a}s Szamuely},
}



@article {merel:intersections,
    AUTHOR = {Merel, L.},
     TITLE = {Intersections sur des courbes modulaires},
   JOURNAL = {Manuscripta Math.},
  FJOURNAL = {Manuscripta Mathematica},
    VOLUME = {80},
      YEAR = {1993},
    NUMBER = {3},
     PAGES = {283--289},
      ISSN = {0025-2611},
     CODEN = {MSMHB2},
   MRCLASS = {14G35 (11G18)},
  MRNUMBER = {94k:14014},
MRREVIEWER = {Douglas L. Ulmer},
}

@article{agashe-stein:bsd,
    author = "Agashe, A. and Stein, W.\thinspace{}A.",
    title  = "Visible Evidence for the Birch and Swinnerton-Dyer Conjecture
              for Modular Abelian Varieties of Analytic Rank~$0$",
    date   = {2001},
    journal = {In Preparation}
}

@article{agashe-stein:visibility,
    author = "Agashe, A. and Stein, W.\thinspace{}A.",
    title = {Visibility of {S}hafarevich-{T}ate {G}roups of {A}belian {V}arieties},
    year = {2002},
    journal = {to appear in J. of Number Theory}
}

@article {kramer:largesha,
    AUTHOR = {Kramer, K.},
     TITLE = {A family of semistable elliptic curves with large
              {T}ate-{S}hafarevitch groups},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {89},
      YEAR = {1983},
    NUMBER = {3},
     PAGES = {379--386},
      ISSN = {0002-9939},
     CODEN = {PAMYAR},
   MRCLASS = {14K07 (11G05 14G25)},
  MRNUMBER = {85d:14059},
MRREVIEWER = {Reinhard B{\"o}lling},
}

@article {cassels:bigsha,
    AUTHOR = {Cassels, J.\thinspace{}W.\thinspace{}S.},
     TITLE = {Arithmetic on curves of genus $1$. {V}{I}. {T}he {T}ate-\v
              {S}afarevi\v c group can be arbitrarily large},
   JOURNAL = {J. Reine Angew. Math.},
    VOLUME = {214/215},
      YEAR = {1964},
     PAGES = {65--70},
   MRCLASS = {14.49 (10.12)},
  MRNUMBER = {29 \#104},
MRREVIEWER = {P. Abellanas},
}


@article {cheryl,
    AUTHOR = {Beaver, Cheryl DeLorme},
     TITLE = {$5$-torsion in the {S}hafarevich-{T}ate group of a family of
              elliptic curves},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {82},
      YEAR = {2000},
    NUMBER = {1},
     PAGES = {25--46},
      ISSN = {0022-314X},
     CODEN = {JNUTA9},
   MRCLASS = {11G05 (11G07)},
  MRNUMBER = {2001d:11059},
MRREVIEWER = {Kenneth Kramer},
}

@article {siman_wong:lots_of_sha,
    AUTHOR = {Wong, Siman},
     TITLE = {Elliptic curves and class number divisibility},
   JOURNAL = {Internat. Math. Res. Notices},
  FJOURNAL = {International Mathematics Research Notices},
      YEAR = {1999},
    NUMBER = {12},
     PAGES = {661--672},
      ISSN = {1073-7928},
   MRCLASS = {11G05 (11R29)},
  MRNUMBER = {2000i:11088},
MRREVIEWER = {Kenneth Kramer},
}

@article {bolling:sha,
    AUTHOR = {B{\"o}lling, Reinhard},
     TITLE = {Die {O}rdnung der {S}chafarewitsch-{T}ate-{G}ruppe kann
              beliebig gro\ss \ werden},
   JOURNAL = {Math. Nachr.},
    VOLUME = {67},
      YEAR = {1975},
     PAGES = {157--179},
   MRCLASS = {14K15},
  MRNUMBER = {52 \#5684},
MRREVIEWER = {J. W. S. Cassels},
}








@book {matsumura,
    AUTHOR = {Matsumura, H.},
     TITLE = {Commutative ring theory},
      NOTE = {Translated from the Japanese by M. Reid},
 PUBLISHER = {Cambridge University Press},
   ADDRESS = {Cambridge},
      YEAR = {1986},
     PAGES = {xiv+320},
      ISBN = {0-521-25916-9},
   MRCLASS = {13-01},
  MRNUMBER = {88h:13001},
MRREVIEWER = {W. V. Vasconcelos},
}









@article {bockle:density,
    AUTHOR = {B{\"o}ckle, Gebhard},
     TITLE = {On the density of modular points in universal deformation
              spaces},
   JOURNAL = {Amer. J. Math.},
  FJOURNAL = {American Journal of Mathematics},
    VOLUME = {123},
      YEAR = {2001},
    NUMBER = {5},
     PAGES = {985--1007},
      ISSN = {0002-9327},
     CODEN = {AJMAAN},
   MRCLASS = {11F80},
  MRNUMBER = {1 854 117},
}

@article {katz:torsion,
    AUTHOR = {Katz, N.\thinspace{}M.},
     TITLE = {Galois properties of torsion points on abelian varieties},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {62},
      YEAR = {1981},
    NUMBER = {3},
     PAGES = {481--502},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {14K15 (10D35 14G05)},
  MRNUMBER = {82d:14025},
MRREVIEWER = {Kenneth A. Ribet},
}

@article {kolyvagin:structure_of_selmer,
    AUTHOR = {Kolyvagin, V. A.},
     TITLE = {On the structure of {S}elmer groups},
   JOURNAL = {Math. Ann.},
  FJOURNAL = {Mathematische Annalen},
    VOLUME = {291},
      YEAR = {1991},
    NUMBER = {2},
     PAGES = {253--259},
      ISSN = {0025-5831},
     CODEN = {MAANA},
   MRCLASS = {11G05 (11G40)},
  MRNUMBER = {93e:11073},
MRREVIEWER = {Massimo Bertolini},
}
