Local-global compatibility at l=p for automorphic Galois representations over CM fields

Abstract: In joint work with Hevesi, Thorne and Whitmore we prove that the Galois representations associated with cohomological cuspidal automorphic representations over CM fields are potentially semi-stable and compatible with the local Langlands correspondence, up to semisimplification. The novelty of our work is that we make no assumptions on residual Galois representation. Our method relies on a bound on the torsion in the cohomology of certain Shimura varieties, which can be seen as a generalisation of the Caraiani-Scholze vanishing theorem.

algebraic geometrynumber theoryrepresentation theory

Audience: researchers in the topic

KIAS HCMC Algebra Seminar

Series comments: This list only contains virtual talks hosted by HCMC Algebra Seminar. For in-person talks, please visit the seminar webpage.