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

作者:   时间:2021-10-09   点击数:

Lecturer: Ouyang Yi

Abstract:Let p be a prime number. KęstutisČesnavičius 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 enablesus 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.

Introduction to the Lecturer:Ouyang Yi, professor of University of Science and Technology of Chin, is engaged in the research of number theory and its application. He was graduated from University of Minnesota in 2000 and returned to China in 2003. He has worked in Tsinghua University and University of Science and Technology of China. He has published more than 30 papers in the basic research of number theory and the application research of elliptic curve homologous cryptography. He is now a member of the school's Teaching Committee and a famous teacher in Anhui Province. He has won the Teaching Achievement Award of the Chinese Academy of Sciences and Anhui Province and the Excellent Teacher Award of Baosteel for the talent training of Hua Luogeng's Science and Technology Elite Program.

Invitee:Zhao Lilu, Professor from School of Mathematics

Time:10:00-11:00, October 26 (Tuesday)

Venue:Tencent Meeting ID: 979 864 372

Hosted by the School of Mathematics, Shandong University

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