Visibility of the Shafarevich-Tate Group at Higher Level Dimitar P. Jetchev
William A. Stein We study visibility of Shafarevich-Tate groups of modular abelian varieties in Jacobians of modular curves of higher level. We prove a theorem about the existence of visible elements at a specific higher level under hypotheses that can be verified explicitely. We also provide a table of examples of visible subgroups at higher level and state conjectures inspired by our data.

Dimitar P. Jetchev Department of Mathematics University of California Berkeley, CA 94720-3840 [email protected] William A. Stein Department of Mathematics University of Washington Seattle, WA 98195-4350 [email protected]

15pt