Potentially semi-stable deformation rings for discrete series extended types

Sandra Rozensztajn

Potentially semi-stable deformation rings for discrete series extended types

Number Theory 2015-10-26 v3

Authors: Sandra Rozensztajn

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-M\'ezard conjecture for these rings. As an application, we give some results on the existence of congruences modulo $p$ for newforms in $S_k(\Gamma_0(p))$ .

Keywords

deformation rings potentially semi-stable discrete series inertial type Breuil-Mézard conjecture Galois representations newforms congruences modulo p

Cite

@article{arxiv.1403.1794,
  title  = {Potentially semi-stable deformation rings for discrete series extended types},
  author = {Sandra Rozensztajn},
  journal= {arXiv preprint arXiv:1403.1794},
  year   = {2015}
}

Comments

Refereed version ; to appear in Journal de l'\'Ecole Polytechnique

Potentially semi-stable deformation rings for discrete series extended types

Abstract

Keywords

Cite

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