Locally analytic completed cohomology of Shimura varieties of Hodge type

Kensuke Aoki

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arXiv · 2508.11099

Locally analytic completed cohomology of Shimura varieties of Hodge type

Kensuke Aoki

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Abstract

For Shimura varieties of Hodge type, we show that there are natural isomorphisms between locally analytic complete cohomology groups and cohomology groups for flag varieties with coefficient which is given by their perfectoid covers. This result is a generalization of that of Pan for the modular curve and Qiu-Su for unitary Shimura curves.

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Kensuke Aoki. 2025-08-14. Locally analytic completed cohomology of Shimura varieties of Hodge type. https://arxiv.org/abs/2508.11099

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