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Summary: Visibility of Shafarevich-Tate 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 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 de-
scribe a construction of visible elements of certain Shafarevich-Tate groups. This
construction can be used to give some of the rst 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.
Key Words: Visibility, Shafarevich-Tate Group, Birch and Swinnerton-
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