% macros for bsd.tex extracted from macros.tex

\newcommand{\defn}[1]{{\em #1}}
\newcommand{\an}{{\rm an}}
\newcommand{\e}{\mathbf{e}}
\newcommand{\Sha}{{\mbox{\textcyr{Sh}}}}
\newcommand{\Sha}{{\cyr X}}
\newcommand{\la}{\leftarrow}
\newcommand{\da}{\downarrow}
\newcommand{\set}[1]{\{#1\}}
\newcommand{\Q}{\mathbb{Q}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\K}{{\mathbb K}}
\newcommand{\dual}{\bot}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\F}{\mathbb{F}}
\newcommand{\h}{\mathfrak{h}}
\newcommand{\p}{\mathfrak{p}}
\newcommand{\m}{\mathfrak{m}}
\newcommand{\pari}{{\sc Pari}}
\newcommand{\magma}{{\sc Magma}}
\newcommand{\hd}[1]{\vspace{1ex}\noindent{\bf #1} }
\renewcommand{\Re}{\mbox{\rm Re}}
\renewcommand{\L}{\mathcal{L}}
\renewcommand{\l}{\ell}
\renewcommand{\t}{\tau}
\renewcommand{\O}{\mathcal{O}}
\renewcommand{\a}{\mathfrak{a}}
\renewcommand{\H}{\HH}
\DeclareMathOperator{\im}{im}
\DeclareMathOperator{\Reg}{Reg}
\DeclareMathOperator{\Sel}{Sel}
\DeclareMathOperator{\Re}{Re}
\DeclareMathOperator{\new}{new}
\DeclareMathOperator{\tor}{tor}
\DeclareMathOperator{\Ker}{Ker}
\DeclareMathOperator{\ord}{ord}