We define deformation rings for potentially semi-stable deformations of fixed discrete series extended type in dimension . In the case of representations of the Galois group of , 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 for newforms in .
Nous définissons des anneaux de déformations pour les déformations potentiellement semi-stables ayant un type étendu de la série discrète fixé en dimension . Dans le cas des représentations du groupe de Galois de , 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 pour les formes nouvelles dans .
Accepted:
DOI: 10.5802/jep.22
Keywords: Galois representations, deformation rings, Breuil-Mézard conjecture
Mot clés : Représentations galoisiennes, anneaux de déformations, conjecture de Breuil-Mézard
Sandra Rozensztajn 1
@article{JEP_2015__2__179_0, 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}, volume = {2}, year = {2015}, doi = {10.5802/jep.22}, mrnumber = {3411395}, zbl = {1330.11039}, language = {en}, url = {https://jep.centre-mersenne.org/articles/10.5802/jep.22/} }
TY - JOUR AU - Sandra Rozensztajn TI - Potentially semi-stable deformation rings for discrete series extended types JO - Journal de l’École polytechnique — Mathématiques PY - 2015 SP - 179 EP - 211 VL - 2 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.22/ DO - 10.5802/jep.22 LA - en ID - JEP_2015__2__179_0 ER -
%0 Journal Article %A Sandra Rozensztajn %T Potentially semi-stable deformation rings for discrete series extended types %J Journal de l’École polytechnique — Mathématiques %D 2015 %P 179-211 %V 2 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.22/ %R 10.5802/jep.22 %G en %F JEP_2015__2__179_0
Sandra Rozensztajn. 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. https://jep.centre-mersenne.org/articles/10.5802/jep.22/
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