Deformation rings and parabolic induction
Journal de Théorie des Nombres de Bordeaux, Tome 30 (2018) no. 2, pp. 695-727.

Nous étudions les déformations des représentations lisses modulo p (et leurs duaux) d’un groupe réductif p-adique G. Sous une hypothèse de généricité faible, nous prouvons que le foncteur d’induction parabolique relatif à un sous-groupe parabolique P=LN induit un isomorphisme entre l’anneau de déformation universel d’une représentation supersingulière σ ¯ de L et de son induite parabolique π ¯. En conséquence, nous montrons que tout relèvement continu de π ¯ est induit à partir d’un unique relèvement continu de σ ¯.

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 σ ¯ of L and of its parabolic induction π ¯. As a consequence, we show that every Banach lift of π ¯ is induced from a unique Banach lift of σ ¯.

Reçu le :
Accepté le :
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DOI : https://doi.org/10.5802/jtnb.1046
Classification : 22E50,  11F70
Mots clés : p-adic reductive groups, smooth representations, 𝔪-adically continuous representations, parabolic induction, deformations
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Julien Hauseux; Tobias Schmidt; Claus Sorensen. Deformation rings and parabolic induction. Journal de Théorie des Nombres de Bordeaux, Tome 30 (2018) no. 2, pp. 695-727. doi : 10.5802/jtnb.1046. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1046/

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