Vincent Pilloni (ENS Lyon)
Coherent cohomology and Galois representations

We prove, under some mild assumptions, that eigensystems occuring in the coherent cohomology of a PEL shimura varieties are p-adic limits of eigensystems coming from cuspidal, regular modular forms. As a consequence, we can associate Galois representations to automorphic forms which are at infinity non-degenerate limits of discrete series. The proof uses some strange formal models introduced by Scholze. This is a joint work with Stroh.