Speaker：Yi Ouyang（University of Science and Technology of China）

Time：2023-2-24, 15:00

Location：Tencent Meeting ID：451-083-833（Password:123456）

Abstract:

Suppose K is a global field, L/K is a cyclic extension and A/K is an abelian variety. In this talk, we prove several unboundedness results of the Tate-Shafarevich groups Sha(A/L) under the conditions that:

 (1) A is a fixed abelian variety over K and L varies over cyclic extensions of K of the same degree, which give an affirmative answer to an open problem proposed by K. Cesnavicius;

 (2) L/K is a fixed cyclic extension, and either K is a number field and A varies over elliptic curves，or the degree of L/K is 2-power and A varies over quadratic twists of a principally polarized abelian variety, which generalize results of K. Matsuno and M. Yu respectively.

This is a joint work with Jianfeng Xie.