Yichao Tian (Strasbourg): On the Beilinson-Bloch-Kato conjecture for Rankin-Selberg motives

Oberseminar, Dec. 12, 2019

In this talk, I will report some recent progress on the rank $0$ case of Beilinson-Bloch-Kato conjecture for Rankin-Selberg motives attached to certain cuspidal automorphic representations of $GL_n\times GL_{n+1}$ over a CM field. More precisely, we show that, under some technical assumptions, the non-vanishing of certain Rankin-Selberg $L$-function implies the vanishing of the corresponding Selmer group. We got also some partial results in the rank $1$ case. The main ingredients for the proof include Gan-Gross-Prasad conjecture for unitary groups, the geometry of unitary Shimura varieties and Kolyvagin’s machinery of Euler systems. This is a joint work with Yifeng Liu, Liang Xiao, Wei Zhang and Xinwen Zhu.