Resumen de On modular weights of Galois representations

Michael M. Schein

• Let $F$ be a totally real field and $\rho: \Gal(\overline{F}/F) \to \GL_2(\Fpbar)$ a Galois representation whose restriction to a decomposition group at some place dividing $p$ is irreducible. Suppose that $\rho$ is modular of some weight $\sigma$. We specify a set of weights, not containing $\sigma$, such that $\rho$ is modular for at least one weight in this set.