Visibility of Shafarevich-Tate Groups of Abelian Varieties

William A. Stein

Amod Agashe


We investigate Mazur's notion of visibility of elements of Shafarevich-Tate groups of abelian varieties. We give a proof that every cohomology class is visible in a suitable abelian variety, discuss the visibility dimension, and describe a construction of visible elements of certain Shafarevich-Tate groups. This construction can be used to give some of the first evidence for the Birch and Swinnerton-Dyer Conjecture for abelian varieties of large dimension. We then give examples of visible and invisible Shafarevich-Tate groups.

This paper has appeared in Journal of Number Theory, 97 (2002), no. 1, 171--185. Here is the JNT version of the paper.
visibility_of_sha_v6.dvi      visibility_of_sha_v6.tex

ps   pdf   html