Seminar: Non-archimedean geometry

Pierre Colmez (CNRS, Sorbonne Université, Paris)

Abstract: Emerton has given a factorization of the completed cohomology of the tower of modular curves, separating the contributions of all the groups that act (i.e., the absolute Galois group of ${\mathbb Q}$ and the ${\mathrm GL}_2({\mathbb Q}_\ell)$ for all primes $\ell$).
I will explain how one can use p-adic Hodge theory to construct a Kirillov model for the completed cohomology and obtain a more direct construction of this factorization.