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

Abstract

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 $K$ is a totally real number field. We prove new cases of this conjecture when $k={\mathbb{F}}_5$ by using the automorphy lifting theorems over CM fields established in previous work of the authors.

arXiv comment11 pages. Refereed version

References in corpus (7)

• On Serre's conjecture for mod l Galois representations over totally real fields
• Congruences between Hilbert modular forms: constructing ordinary lifts
• Modularity of nearly ordinary 2-adic residually dihedral Galois representations
• On two dimensional weight two odd representations of totally real fields
• Serre's conjecture over F_9
• Automorphy of some residually S_5 Galois representations
• Modularity of ${\mathrm{GL}}_2({\mathbb{F}}_p)$-representations over CM fields