Locally analytic completed cohomology

Published 30 Aug 2022 in math.NT | (2209.01057v2)

Abstract: We compute the geometric Sen operator for arbitrary Shimura varieties in terms of equivariant vector bundles of flag varieties and the Hodge-Tate period map. As an application, we obtain the rational vanishing of completed cohomology in the Calegari-Emerton conjectures.

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J. E. Rodríguez Camargo

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