Current Developments in Mathematics
Geometric Satake, categorical traces, and arithmetic of Shimura varieties
Pages: 145 – 206
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.