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arxiv: 2209.01057 · v4 · submitted 2022-08-30 · 🧮 math.NT

Locally analytic completed cohomology

J. E. Rodr\'iguez Camargo This is my paper
classification 🧮 math.NT
keywords cohomologycompletedvarietiesanalyticapplicationarbitrarybundlescalegari-emerton
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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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