Current Developments in Mathematics

Volume 2016

Geometric Satake, categorical traces, and arithmetic of Shimura varieties

Pages: 145 – 206



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


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.

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

Published 9 May 2018