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Visibility of Shafarevich–Tate Groups of Abelian Varieties

✍ Scribed by Amod Agashe; William Stein

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
171 KB
Volume
97
Category
Article
ISSN
0022-314X

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✦ Synopsis

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.

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