For Shimura varieties of Hodge type, locally analytic completed cohomology is naturally isomorphic to cohomology of flag varieties with locally analytic sheaves from perfectoid covers.
Deligne,Travaux de Shimura, Séminaire Bourbaki, 23ème année (1970/1971), Exp
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Locally analytic completed cohomology of Shimura varieties of Hodge type
For Shimura varieties of Hodge type, locally analytic completed cohomology is naturally isomorphic to cohomology of flag varieties with locally analytic sheaves from perfectoid covers.