Title :

Deformation rings and parabolic induction

Author(s) :

Hauseux, Julien [Auteur correspondant]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Schmidt, Tobias [Auteur]
Institut de Recherche Mathématique de Rennes [IRMAR]
Sorensen, Claus [Auteur]
Department of Mathematics [Univ California San Diego] [MATH - UC San Diego]

Journal title :

Journal de Théorie des Nombres de Bordeaux

Pages :

695-727

Publisher :

Société Arithmétique de Bordeaux

Publication date :

2018-12-06

ISSN :

2118-8572

English keyword(s) :

p-adic reductive groups
smooth representations
m-adically continuous representations
parabolic induction
deformations

HAL domain(s) :

Mathématiques [math]/Théorie des représentations [math.RT]
Mathématiques [math]/Théorie des nombres [math.NT]

English abstract : [en]

We study deformations of smooth mod $p$ representations (and their duals) of a $p$-adic reductive group $G$. Under some mild genericity condition, we prove that parabolic induction with respect to a parabolic subgroup ...
Show more >We study deformations of smooth mod $p$ representations (and their duals) of a $p$-adic reductive group $G$. Under some mild genericity condition, we prove that parabolic induction with respect to a parabolic subgroup $P=LN$ defines an isomorphism between the universal deformation rings of a supersingular representation $\bar{\sigma}$ of $L$ and of its parabolic induction $\bar{\pi}$. As a consequence, we show that every Banach lift of $\bar{\pi}$ is induced from a unique Banach lift of $\bar{\sigma}$.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL