Modularity of ${\mathrm{PGL}}_2({\mathbb{F}}_p)$-representations over totally real fields

Patrick B. Allen, Chandrashekhar B. Khare, Jack A. Thorne

We study an analogue of Serre's modularity conjecture for projective representations $\overline{\rho }:\mathrm{Gal}(\overline{K}/K)\to {\mathrm{PGL}}_2(k)$, where $…