Visibility of Shafarevich-Tate Groups of Abelian Varieties
Amod Agashe
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.
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
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