Potentially semi-stable deformation rings for discrete series extended types
[Anneaux de déformations potentiellement semi-stables pour les types étendus de la série discrète]
Journal de l’École polytechnique — Mathématiques, Tome 2 (2015) , pp. 179-211.

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)).

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)).

Reçu le : 2015-05-10
Accepté le : 2015-09-14
DOI : https://doi.org/10.5802/jep.22
Classification : 11F80,  11F33
Mots clés: Représentations galoisiennes, anneaux de déformations, conjecture de Breuil-Mézard
@article{JEP_2015__2__179_0,
     author = {Sandra Rozensztajn},
     title = {Potentially semi-stable deformation rings for discrete series extended types},
     journal = {Journal de l'\'Ecole polytechnique --- Math\'ematiques},
     pages = {179--211},
     publisher = {\'Ecole polytechnique},
     volume = {2},
     year = {2015},
     doi = {10.5802/jep.22},
     zbl = {1330.11039},
     mrnumber = {3411395},
     language = {en},
     url = {jep.centre-mersenne.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, Tome 2 (2015) , pp. 179-211. doi : 10.5802/jep.22. https://jep.centre-mersenne.org/item/JEP_2015__2__179_0/

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