# On the automorphy of 2-dimensional potentially semistable deformation rings of $G_{Q_p}$

• Shen-Ning Tung (Universität Duisburg-Essen)
• Tuesday 22 May 2018, 14:30-15:30
• MR13.

Using p-adic local Langlands correspondence for GL2 , we prove that the support of patched modules constructed by Caraiani, Emerton, Gee, Geraghty, Paskunas, and Shin meet every irreducible component of the potentially semistable deformation ring. This gives a new proof of the Breuil-Mézard conjecture for 2-dimensional representations of the absolute Galois group of Qp when p>2, which is new in the case p=3 and $\bar{r}$ a twist of an extension of the trivial character by the mod p cyclotomic character. As a consequence, a local restriction in the proof of Fontaine-Mazur conjecture by Kisin is removed.

This talk is part of the Number Theory Seminar series.