On the Hodge-Tate period map for Shimura varieties of Hodge type

The Hodge-Tate period map is an important, new tool for studying the geometry of Shimura varieties, p-adic automorphic forms and torsion classes in the cohomology of Shimura varieties. It is a G(A_f)-equivariant map from a perfectoid Shimura variety into a flag variety with only an action of G(Q_p) and can be thought of as a p-adic analogue of the Borel embedding. In this talk, I will describe a canonical construction of the Hodge-Tate period map and of automorphic vector bundles for Shimura varieties of Hodge type. This is part of ongoing joint work with Peter Scholze.

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