Finite length for cohomological mod p representations of GL2 of a p-adic field

Abstract: In the search for a mod p local Langlands correspondence, it is natural to study the representations of GL2 of a p-adic field F in the mod p cohomology of Shimura curves. It is expected that the action of GL2(F) on a Galois-isotypic subspace of the mod p cohomology of a tower of Shimura curves (of fixed tame level) has finite length and is related to the local Galois representation at p. In the case of modular curves, this is known by the local-global compatibility theorem of Emerton. I'll explain how to prove some new cases of the finiteness of the length when F is an unramified extension of Qp. This finiteness is related to the computation of the Gelfand-Kirillov dimension of these representations. This is a joint work with Christophe Breuil, Florian Herzig, Yongquan Hu and Stefano Morra.

commutative algebraalgebraic geometrynumber theory

Audience: researchers in the topic

Recent Advances in Modern p-Adic Geometry (RAMpAGe)

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