Locally analytic completed cohomology of Shimura varieties of Hodge type

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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ArXiv.org
Published
2025-08-14
Primary Topic
Prenatal Screening and Diagnostics
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article

Locally analytic completed cohomology of Shimura varieties of Hodge type

ArXiv.org
Prenatal Screening and Diagnostics
article

Locally analytic completed cohomology of Shimura varieties of Hodge type

article en

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.

ArXiv.org
Openalex Percentile: Top 34%
Prenatal Screening and Diagnostics
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Locally analytic completed cohomology of Shimura varieties of Hodge type · ArXiv.org (2025) | TGRS Research Map | TGRS