On the Hodge-Tate period map for Shimura varieties of Hodge type
Automorphic forms, Shimura varieties, Galois representations and L-functions December 01, 2014 - December 05, 2014
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC Secondary Mathematics Subject Classification No Secondary AMS MSC
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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