On the automorphy of 2-dimensional potentially semi-stable deformation rings of $G_{{\mathbb{Q}}_p}$

Shen-Ning Tung

Using $p$-adic local Langlands correspondence for ${\mathrm{GL}}_2({\mathbb{Q}}_p)$, we prove that the support of patched modules constructed by Caraiani, Emerton, Gee, Geraghty,…