Sur les -blocs de niveau zéro des groupes -adiques
Keyword(s):
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.
2020 ◽
Vol 16
(07)
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pp. 1449-1491
2016 ◽
Vol 138
(3)
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pp. 657-682
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2013 ◽
Vol 20
(3)
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pp. 489-500
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2014 ◽
Vol 47
(4)
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pp. 655-722
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