Central elements in affine mod $p$ Hecke algebras via perverse $\mathbb{F}_p$-sheaves
| Autor: | Cass, Robert |
|---|---|
| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Compositio Mathematica 157 (2021), 2215-2241 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1112/S0010437X2100751X |
| Popis: | Let $G$ be a split connected reductive group over a finite field of characteristic $p > 2$ such that $G_\text{der}$ is absolutely almost simple. We give a geometric construction of perverse $\mathbb{F}_p$-sheaves on the Iwahori affine flag variety of $G$ which are central with respect to the convolution product. We deduce an explicit formula for an isomorphism from the spherical mod $p$ Hecke algebra to the center of the Iwahori mod $p$ Hecke algebra. We also give a formula for the central integral Bernstein elements in the Iwahori mod $p$ Hecke algebra. To accomplish these goals we construct a nearby cycles functor for perverse $\mathbb{F}_p$-sheaves and we use Frobenius splitting techniques to prove some properties of this functor. We also prove that certain equal characteristic analogues of local models of Shimura varieties are strongly $F$-regular, and hence they are $F$-rational and have pseudo-rational singularities. Comment: Final version |
| Databáze: | arXiv |
| Externí odkaz: |
|