Shafarevich-Tate Groups

This monograph explores the finiteness and structure of Shafarevich-Tate groups of abelian varieties over global fields of any characteristic. Readers will better understand how the methods of Euler systems and Kolyvagin systems can be adapted to Heegner points and CM points. Also offered is a comprehensive overview of the most important classical and recent results on these objects. Shafarevich-Tate Groups will be a valuable resource to those interested in this active area of research.

Preliminaries.- Elliptic curves; Drinfeld modules; Shimura curves, Elliptic spaces.- Complex multiplication, Heegner points, CM points.- Local fields and local conditions.- Global fields and Selmer structures.- Euler systems.- Kolyvagin systems.- Selmer groups and Kolyvagin systems.