Visibility of Shafarevich-Tate Groups of Abelian Varieties |
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| Authors: | Amod AgasheWilliam Stein |
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| Institution: | a Department of Mathematics, University of Texas, Austin, Texas, 78712, f1amod@math.utexas.eduf1b Department of Mathematics, Harvard University, Cambridge, Massachusetts, f2was@math.harvard.eduf2 |
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| 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. |
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| Keywords: | visibility Shafarevich-Tate group Birch and Swinnerton-Dyer conjecture modular abelian variety |
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