Anticyclotomic Iwasawa theory for Rankin-Selberg products
Prof. Yifeng Liu
2023-12-19
MCM110
Speaker: Prof. Yifeng Liu (Zhejiang University)Time: 14:00-16:00 Dec. 15 (Friday), Video 9:30-11:30 Dec. 18 (Monday), Video, 9:30-11:30 Dec. 19 (Tuesday), Video. Place: MCM110 & Online (Zoom ID: 3329836068 Password: mcm1234)
Title: Anticyclotomic Iwasawa theory for Rankin-Selberg products
Abstract: Recently I have constructed the anticyclotomic p-adic L-functions for certain automorphic representations of GL(n)xGL(n+1) over CM fields, based on the complete attack on the global Gan-Gross-Prasad conjecture for unitary groups, and formulated the corresponding Iwasawa main conjectures (arXiv:2306.07039). In a joint work in process with Yichao Tian and Liang Xiao, we prove in many cases one side of the divisibility in the main conjectures for both root numbers. This result generalizes earlier works by Bertolini-Darmon and Howard in the case of GL(1)xGL(2), and also upgrades the previous work of Liu-Tian-Xiao-Zhang-Zhu on the Beilinson-Bloch-Kato conjecture to the Iwasawa level. In this mini course, I will go through the proof when the root number is +1 for a scenario governed by GL(2)xGL(3) .
