Locally analytic completed cohomology of Shimura varieties of Hodge type

TL;DR

This paper establishes natural isomorphisms between locally analytic completed cohomology and flag variety cohomology for Hodge type Shimura varieties, extending previous results from modular and unitary cases.

Contribution

It generalizes existing isomorphism results to a broader class of Shimura varieties of Hodge type using perfectoid covers.

Findings

Isomorphisms between cohomology groups established

Extension of Pan's and Qiu-Su's results to Hodge type varieties

Framework applicable to a wide class of Shimura varieties

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.