Current Developments in Mathematics

Volume 2016

Geometric Satake, categorical traces, and arithmetic of Shimura varieties

Pages: 145 – 206

DOI: http://dx.doi.org/10.4310/CDM.2016.v2016.n1.a4

Author

Xinwen Zhu (Department of Mathematics, California Institute of Technology, Pasadena, Cal., U.S.A.)

Abstract

We survey some recent work on the geometric Satake of $p$-adic groups and its applications to some arithmetic problems of Shimura varieties. We reformulate a few constructions appeared in the previous works more conceptually.

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The author was partially supported by NSF grant DMS-1602092 and the Sloan Fellowship.