Modern Mathematics Lecture Series | Beilinson--Bloch--Kato Conjecture and Iwasawa theory for Rankin--Selberg motives

Abstract

Beilinson--Bloch--Kato conjecture and Iwasawa main conjecture can be viewed as generalizations and p-adic analogues of the celebrated BSD conjecture for elliptic curves. These conjectures predict deep relations between the L-function (or its p-adic analogue) of a motive with some arithmetic invariants. In this talk, I will first start with some review on more classical results and basic ideas in the case of elliptic curves, and then I will discuss some recent progress of those two conjectures for Rankin--Selberg motives of type GL_n*GL_{n+1} over a CM field. This talk is based on my joint work with Yifeng Liu, Liang Xiao, Wei Zhang and Xinwen Zhu.

About the speaker

Yichao Tian 田一超

MCM, CAS

I am now a faculty member at the Moringside Center of Mathematics, AMSS, Chinese Academy of Sciences. I am working on arithmetic algebraic geometry, and particularly interested in p-divisible groups, p-adic Hodge theory, p-adic modular forms, and the geometry of Shimura varieties in characteristic p.

Homepage：

http://www.mcm.ac.cn/people/members/202108/t20210820_658104.html