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.
Carayol,Sur la mauvaise réduction des courbes de Shimura, Compositio Math.59 (1986), no
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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.