Anticyclotomic Iwasawa Main Conjecture for Rankin—Selberg motives

Yichao Tian
Morningside Center of Mathematics
http://www.mcm.ac.cn/faculty/tianyichao/201409/t20140916_255897.html

Date(s) : 03/06/2025 iCal
14h00 - 15h00

Let M be the Rankin—Selberg motive arising from a pair of regular algebraic conjugate self-dual cuspidal automorphic representations of minimal weight on GL_n and GL_{n+1} over a CM number field F. Let F_{\infty}/F be an anti-cyclotomic Z_p^d-extension such that M is good ordinary at all p-adic primes ramified in F_{\infty}. In this talk, I will explain that under some technical assumptions, the characteristic ideal of the Bloch—Kato Iwasawa Selmer module for M along F_{\infty}/F contains the corresponding p-adic L-function, constructed previously by Yifeng Liu. A key step in the proof is to construct a version of bipartite Euler system for such Rankin—Selberg motives using the geometry of unitary Shimura varieties. This is a joint work with Yifeng Liu and Liang Xiao.