| Résume | Let $G$ be a $p$-adic reductive group. Let $C$ be an algebraic
closure of the field of $\ell$ elements where $\ell$ is a prime distinct
from $p$, and $W(C):=Z_{\ell}^{ur}$ be its Witt ring. Consider an
irreducible admissible $C$-representation $\pi$ of $G$. Our goal is to
discuss its Brauer character that we expect as a $W(C)$-coefficient
distribution on a "prime-to-$\ell$" subset of $G$.
We will discuss the Harish-Chandra--Howe local character expansions of
the Brauer character constructed by Dat and Vignéras on compact mod
center elements, some partial construction of the Brauer character on
non-compact elements, and further conjectural properties. |
