Visibility of Shafarevich–Tate Groups of Abelian Varieties Original Research Article

We investigate Mazurʹs 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.