Potentially semi-stable deformation rings for discrete series extended types

Sandra Rozensztajn

doi:10.5802/jep.22

Potentially semi-stable deformation rings for discrete series extended types
[Anneaux de déformations potentiellement semi-stables pour les types étendus de la série discrète]

Sandra Rozensztajn ¹

¹ UMPA, ÉNS de Lyon, UMR 5669 du CNRS 46, allée d’Italie, 69364 Lyon Cedex 07, France

Journal de l’École polytechnique — Mathématiques, Tome 2 (2015), pp. 179-211.

Résumé
Abstract

Nous définissons des anneaux de déformations pour les déformations potentiellement semi-stables ayant un type étendu de la série discrète fixé en dimension $2$ . Dans le cas des représentations du groupe de Galois de $ℚ_{p}$ , nous prouvons un analogue de la conjecture de Breuil-Mézard pour ces anneaux. Nous donnons comme application de ceci des résultats sur l’existence de congruences modulo $p$ pour les formes nouvelles dans $S_{k} (Γ_{0} (p))$ .

We define deformation rings for potentially semi-stable deformations of fixed discrete series extended type in dimension $2$ . In the case of representations of the Galois group of $ℚ_{p}$ , we prove an analogue of the Breuil-Mézard conjecture for these rings. As an application, we give some results on the existence of congruences modulo $p$ for newforms in $S_{k} (Γ_{0} (p))$ .

Reçu le : 2015-05-09
Accepté le : 2015-09-13

MR Zbl

DOI : 10.5802/jep.22

Classification : 11F80, 11F33
Keywords: Galois representations, deformation rings, Breuil-Mézard conjecture
Mot clés : Représentations galoisiennes, anneaux de déformations, conjecture de Breuil-Mézard

Affiliations des auteurs :

Sandra Rozensztajn ¹

¹ UMPA, ÉNS de Lyon, UMR 5669 du CNRS 46, allée d’Italie, 69364 Lyon Cedex 07, France

Licence :

CC-BY-ND 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Sandra Rozensztajn},
     title = {Potentially semi-stable deformation rings for discrete series extended types},
     journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
     pages = {179--211},
     publisher = {\'Ecole polytechnique},
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     year = {2015},
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Sandra Rozensztajn. Potentially semi-stable deformation rings for discrete series extended types. Journal de l’École polytechnique — Mathématiques, Tome 2 (2015), pp. 179-211. doi : 10.5802/jep.22. https://jep.centre-mersenne.org/articles/10.5802/jep.22/

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