一、题目

The growth of Tate-Shafarevich groups in Z/pZ-extensions

二、主讲人

欧阳毅

三、摘要

Let p be a prime number. Kęstutis Česnavičius proved that for an abelian variety A over a global field K, the p-Selmer group Selp(A/L) grows unboundedly when L ranges over the Z/pZ-extensions of K. Moreover, he raised a further problem: is the dimension of Sha(A/L)[p] also unbounded under the above conditions? In this talk we give a positive answer to this problem in the case p not equal char K. This result enable us to generalize the work of Clark, Sharif and Creutz on the growth of potential Sha in cyclic extensions. We also answer a problem poposed by Lim and Murty concerning the growth of the fine Tate-Shafarevich groups. This is joint work with Jianfeng Xie.

四、主讲人简介

欧阳毅，中国科学技术大学教授，从事数论及其应用研究工作。2000年博士毕业于美国明尼苏达大学，2003年回国，先后在清华大学和中国科学技术大学工作。在数论基础研究和椭圆曲线同源密码等应用研究方面共发表论文30多篇。现任校教学委员会委员，是安徽省教学名师，因华罗庚科技英才班人才培养获中科院和安徽省教学成果奖，获宝钢优秀教师奖。

五、邀请人

赵立璐 数学学院教授

六、时间

10月26日（周二）10:00-11:00

七、地点

腾讯会议，会议ID：979 864 372

八、主办方

山东大学数学学院