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Article Dans Une Revue Journal de Théorie des Nombres de Bordeaux Année : 2018

Deformation rings and parabolic induction

Résumé

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 $\bar{\sigma}$.

Dates et versions

hal-01355156 , version 1 (22-08-2016)

Identifiants

Citer

Julien Hauseux, Tobias Schmidt, Claus Sorensen. Deformation rings and parabolic induction. Journal de Théorie des Nombres de Bordeaux, 2018, 30 (2), pp.695-727. ⟨10.5802/jtnb.1046⟩. ⟨hal-01355156⟩
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