Potentially semi-stable deformation rings for discrete series extended types
Journal de l’École polytechnique - Mathématiques, Volume 2  (2015), p. 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 : https://doi.org/10.5802/jep.22
Classification:  11F80,  11F33
Keywords: Galois representations, deformation rings, Breuil-Mézard conjecture
@article{JEP_2015__2__179_0,
     author = {Rozensztajn, Sandra},
     title = {Potentially semi-stable deformation rings for discrete series extended types},
     journal = {Journal de l'\'Ecole polytechnique - Math\'ematiques},
     publisher = {Ecole polytechnique},
     volume = {2},
     year = {2015},
     pages = {179-211},
     doi = {10.5802/jep.22},
     language = {en},
     url = {http://www.numdam.org/item/JEP_2015__2__179_0}
}
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://www.numdam.org/item/JEP_2015__2__179_0/

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