Potentially semi-stable deformation rings for discrete series extended types

[Anneaux de déformations potentiellement semi-stables pour les types étendus de la série discrète]

Rozensztajn, Sandra

Journal de l'École polytechnique - Mathématiques, Tome 2 (2015), p. 179-211 / Harvested from Numdam

Résumé

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 $\mathbb{Q}_p$, 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 $S_k(\Gamma _0(p))$.

Abstract

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 $\mathbb{Q}_p$, 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 $S_k(\Gamma _0(p))$.

Détail

Publié le : 2015-01-01
DOI : https://doi.org/10.5802/jep.22
Classification:  11F80,  11F33
Mots clés: Représentations galoisiennes, anneaux de déformations, conjecture de Breuil-Mézard

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