Title: Unboundedness of Tate-Shafarevich groups in cyclic extensions
Speaker: Prof. Yi Ouyang（欧阳毅）
Affiliation: University of Science and Technology of China（中国科学技术大学）
Time: 14:00-15:00, Friday, Nov 25th, 2022 (UTC+8, Beijing Time)
Venue：腾讯会议/VooV Meeting：610-274-748
入会链接：https://meeting.tencent.com/dm/QUMvf4mZtXUi
Inviter: Chao ZHANG （张超）， Hao ZHANG （张浩）
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 unboundedness results of the Tate-Shafarevich groups Sha(A/L) under the following conditions:
（1）if A is fixed and L varies, which gave an affirmative answer to an open problem proposed by Cesnavicius;
（2）if L/K is fixed and either K is a number field and A varies over elliptic curves，or [L:K]=2-power and A varies over principally polarized abelian varieties, which generalize results of K. Matsuno and M. Yu respectively.
This is a joint work with Jianfeng Xie.
Speaker
欧阳毅，中国科学技术大学数学系教授。2000年博士毕业于美国明尼苏达大学，师从Greg W.Anderson教授。2003年回国在清华大学任职，2007年入职中科大，任教授。在数论与算术几何，及其在密码与编码的应用领域发表论文30余篇。与Jean-Marc Fontaine教授合写待出版论著“Theory of p-adic Galois Representations”。2018年被评为安徽省教学名师，曾获宝钢优秀教师奖。