Unboundedness of Tate-Shafarevich groups in cyclic extensions
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：欧阳毅（中国科学技术大学）
：2023-02-24 15:00
：腾讯会议ID：451-083-833（密码：123456）
报告人：欧阳毅（中国科学技术大学）
时 间：2月24日下午15:00-16:30
地 点：腾讯会议ID：451-083-833（密码：123456）
内容摘要:
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.
个人简介：
欧阳毅，中国科学技术大学数学系教授，博士生导师。中国科大学士（1993）、硕士（1995），美国明尼苏达大学博士（2000）。毕业后在加拿大多伦多大学和清华大学工作。主要研究方向为代数数论和算术代数几何,论文发表在Crelle, Compositio Math., Pub. Mat., Sci. China Math., FFA, DCC等国际学术期刊上。2018年被评为安徽省教学名师，并荣获2017年宝钢优秀教师奖和2022年霍英东教育教学奖等荣誉。
联系人：易少云
