Potentially semi-stable deformation rings for discrete series extended types

Abstract

We define deformation rings for potentially semi-stable deformations of fixed discrete series inertial type in dimension $2$. In the case of representations of the Galois group of ${\mathbf{Q}}_p$, 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 $S_k({\Gamma }_0(p))$.

arXiv commentRefereed version ; to appear in Journal de l'École Polytechnique