Visibility of the Shafarevich-Tate group at higher level
Dimitar P. Jetchev
Department of Mathematics, University of California, Berkeley, CA 94720-3840, USAWilliam A. Stein
Department of Mathematics, University of Washington, Seattle, WA 98195-4350, USA

Abstract
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 certain hypothesis which can be verified explicitly. We also provide a table of examples of visible subgroups at higher level and state a conjecture inspired by our data.
Cite this article
Dimitar P. Jetchev, William A. Stein, Visibility of the Shafarevich-Tate group at higher level. Doc. Math. 12 (2007), pp. 673–696
DOI 10.4171/DM/238