Potentially semi-stable deformation rings for discrete series extended types
Journal de l’École polytechnique — Mathématiques, Volume 2 (2015), pp. 179-211.

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 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)).

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 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)).

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
Rozensztajn, Sandra 1

1 UMPA, ÉNS de Lyon, UMR 5669 du CNRS 46, allée d’Italie, 69364 Lyon Cedex 07, France
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Rozensztajn, Sandra. Potentially semi-stable deformation rings for discrete series extended types. Journal de l’École polytechnique — Mathématiques, Volume 2 (2015), pp. 179-211. doi : 10.5802/jep.22. http://archive.numdam.org/articles/10.5802/jep.22/

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