The de Rham Property of Automorphic Galois Representations over CM Fields

par Lambert A'Campo (IHES)

jeudi 11 déc. 2025, 11:00 → 12:30 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

In joint work in progress with Hevesi, Thorne and Whitmore, we prove that automorphic Galois representations over CM fields are de Rham and have the expected Hodge--Tate weights. The novelty of our result is that we do not impose any assumptions on the residual mod p Galois representation. To achieve this, we prove a theorem on the cohomology of certain unitary Shimura varieties, which gives a bound on the maximal order of a torsion class in the lower half of degrees of cohomology. After placing this theorem in the right context and discussing its proof, I will sketch how it relates to the de Rham property of automorphic Galois representations.

 

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