 
Summary: Visibility of ShafarevichTate Groups of
Abelian Varieties
Amod Agashe
University of Texas
Austin, TX
agashe@math.utexas.edu
and
William Stein
Harvard University
Cambridge, MA
was@math.harvard.edu
Version: February 27, 2002
We investigate Mazur's notion of visibility of elements of ShafarevichTate
groups of abelian varieties. We give a proof that every cohomology class is
visible in a suitable abelian variety, discuss the visibility dimension, and de
scribe a construction of visible elements of certain ShafarevichTate groups. This
construction can be used to give some of the rst evidence for the Birch and
SwinnertonDyer Conjecture for abelian varieties of large dimension. We then
give examples of visible and invisible ShafarevichTate groups.
Key Words: Visibility, ShafarevichTate Group, Birch and Swinnerton
