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Locally analytic completed cohomology (2209.01057v2)
Published 30 Aug 2022 in math.NT
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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