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Sur les
$\ell$ -blocs de niveau zéro des groupes 
$p$ -adiques
- Part of
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- Journal:
- Compositio Mathematica / Volume 154 / Issue 7 / July 2018
- Published online by Cambridge University Press:
- 24 May 2018, pp. 1473-1507
- Print publication:
- July 2018
-
- Article
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Let
$G$ be a 
$p$ -adic group that splits over an unramified extension. We decompose 
$\text{Rep}_{\unicode[STIX]{x1D6EC}}^{0}(G)$ , the abelian category of smooth level 
$0$ representations of 
$G$ with coefficients in 
$\unicode[STIX]{x1D6EC}=\overline{\mathbb{Q}}_{\ell }$ 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.
