On locally analytic vectors of the completed cohomology of Shimura varieties; a generalization of Lue Pan's work

Abstract: In this talk we discuss a natural generalization of Pan's work on locally analytic vectors of completed cohomology. We will sketch how Sen theory provides the bridge between D-modules over the flag variety and the Hodge-Tate cohomology of Shimura varieties via the Hodge-Tate period map. We will prove that the same method apply for the cohomology with compact supports and their duals, obtaining a description of all different completed cohomologies as the analytic cohomology of certain (locally analytic) sheaves over the infinite level Shimura variety. We shall mention how the understanding of D-modules over the flag variety can be helpful to describe the Lie algebra action over the locally analytic completed cohomology.

algebraic geometrynumber theory

Audience: researchers in the topic

Comments: Access code is a(8) where a(n) = 5*a(n-1) + 3 with a(0) = 1.

Séminaire de géométrie arithmétique et motivique (Paris Nord)