Potentially semi-stable deformation rings for discrete series extended types
Anneaux de déformations potentiellement semi-stables pour les types étendus de la série discrète
Résumé
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 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 (Γ 0 (p)).