Lambert A'Campo: Local-global compatibility at l=p for automorphic Galois representations over CM fields

Number Theory Seminar: Lambert A'Campo (IHES)

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

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.