Kojiro Matsumoto
University of Tokyo
Title
Potential automorphy and its application to local-global compatibility
Abstract
In 2014, Harris-Lan-Taylor-Thorne constructed the l-adic Galois representations corresponding to cohomological cuspidal automorphic representations of GLn over CM fields. The compatibility of this construction with the local Langlands correspondence was proved up to semisimplification at all non-l-adic places by Varma (2014). However, compatibility for the monodromy operators was known only in the conjugate self-dual cases and certain special 2-dimensional cases. In this talk, I will explain how to prove local-global compatibility in some self-dual cases and in some sufficiently regular weight cases by using new potential automorphy theorems. Moreover, I will explain how to prove the Ramanujan conjecture for the cohomological cuspidal automorphic representations of GL2 over CM fields. This conjecture was previously proved in the parallel weight case by Boxer-Calegari-Gee-Newton-Thorne (2023).