# Finitude pour les representations lisses de groupes p-adiques

Abstract : We study basic properties of the category of smooth representations of a p-adic group G with coefficients in any commutative ring R in which p is invertible. Our main purpose is to prove that Hecke algebras are noetherian whenever R is ; a question left open since Bernstein's fundamental work for R=C. In a first step, we prove that this noetherian property would follow from a generalization of the so-called Bernstein's second adjointness property between parabolic functors for complex representations. Then, to attack this second adjointness, we introduce and study parahoric functors" between representations of groups of integral points of smooth integral models of G and of their Levi" subgroups. Applying our general study to Bruhat-Tits parahoric models, we get second adjointness for minimal parabolic groups. For non-minimal parabolic subgroups, we have to restrict to classical and linear groups, and use smooth models associated with Bushnell-Kutzko and Stevens semi-simple characters. According to recent announcements by Kim and Yu, the same strategy should also work for tame groups", using Yu's generic characters.
Mots-clés :
Type de document :
Pré-publication, Document de travail
42 pages. 2006
Domaine :

Littérature citée [25 références]

https://hal.archives-ouvertes.fr/hal-00085832
Contributeur : Jean-Francois Dat <>
Soumis le : vendredi 14 juillet 2006 - 22:53:03
Dernière modification le : mardi 22 mai 2018 - 20:40:03
Document(s) archivé(s) le : mardi 6 avril 2010 - 00:10:44

### Citation

Jean-Francois Dat. Finitude pour les representations lisses de groupes p-adiques. 42 pages. 2006. 〈hal-00085832〉

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