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# On Emerton’s factorization of completed cohomology

## May 30 at 14:00 – 16:00 CEST

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.