Wei ZHANG - Selmer Groups for Rankin-Selberg L-functions of GL(2)xGL(3)
Channel: Institut des Hautes Études Scientifiques (IHÉS)
Date: 01/02/2019

LetΠ (resp. Σ) bea cohomological (for the trivial coefficient) cuspidal automorphic representation of  GL(3)  (resp.  GL(2))  over  a  CM  number  field,  and  assume that  they  are  base  change  from  unitary groups.We prove the following theorem:if the Rankin-Selberg L-functionL(Π×Σ, s) does not vanish at its center, then the associatedℓ-adic Bloch-Kato Selmer group vanishes (for primesℓwherethe modℓGalois representations satisfy certain mild conditions). Theconditions onℓcome from Euler system type argument. We will discuss some examples from elliptic curves. This is a joint work with Yifeng Liu, Yichao Tian, Liang Xiao, and Xinwen Zhu.

Vidéo réalisée avec le soutien du projet AAMOT de l’ERC