Crystalline lifts of two-dimensional mod $p$ automorphic Galois representations

Fred Diamond, Davide A. Reduzzi

We show that a sufficient condition for an irreducible automorphic Galois representation $\rho :G_F\to {\mathrm{GL}}_2({\overline{\mathbf{F}}}_p)$ of a totally real field $F$ to have an autom…