Visibility of Shafarevich-Tate Groups of
Abelian Varieties

Amod Agashe
University of Texas
Austin, TX
[email protected] - William Stein
Harvard University
Cambridge, MA
[email protected]

Date: February 24, 2002

Abstract:

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.