Explicit Serre weights for two-dimensional Galois representations over a ramified base

Misja F. A. Steinmetz

Given a totally real number field $F$ and a mod $p$ Galois representation $\rho :G_F\to {\mathrm{GL}}_2({\bar{\mathbf{F}}}_p)$, we propose an explicit definition of the set of Serre…