Sur les $\ell$-blocs de niveau zéro des groupes $p$-adiques

Abstract

Let $G$ be a $p$-adic group that splits over an unramified extension. We decompose $Re{p}_{\Lambda }^0(G)$, the abelian category of smooth level $0$ representations of $G$ with coefficients in $\Lambda ={\overline{\mathbb{Q}}}_{\ell }$ or ${\overline{\mathbb{Z}}}_{\ell }$, into a product of subcategories indexed by inertial Langlands parameters. We construct these categories via systems of idempotents on the Bruhat-Tits building and Deligne-Lusztig theory. Then, we prove compatibilities with parabolic induction and restriction functors and the local Langlands correspondence.

35 pages, in French, extended from unramified groups to reductive groups that split over an unramified field extension

Cited by in corpus (2)

• Unipotent $\ell$-blocks for simply-connected $p$-adic groups
• Depth zero representations over $\overline{\mathbb{Z}}[\frac{1}{p}]$