JournalsdmVol. 12pp. 673–696

Visibility of the Shafarevich-Tate group at higher level

  • Dimitar P. Jetchev

    Department of Mathematics Department of Mathematics University of California University of Washington Berkeley, CA 94720-3840 Seattle, WA 98195-4350

  • William A. Stein

    Department of Mathematics Department of Mathematics University of California University of Washington Berkeley, CA 94720-3840 Seattle, WA 98195-4350
Visibility of the Shafarevich-Tate group at higher level cover
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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