Visibility of Shafarevich-Tate groups of abelian varieties

[摘要] 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. (C) 2002 Elsevier Science (USA).

[发布日期] 2002-11-01

[关键词] visibility;Shafarevich-Tate group;Birch and Swinnerton-Dyer conjecture;modular abelian variety