2 problems

Let $F^+$ be the relevant totally real field, let $\overline r:G_{F^+}\rightarrow\mathcal{G}_n(\mathbb{F})$ be automorphic, and let $\overline r_p$ be its associated local $L$-homo…

Let $F$ be a totally real field, let $p$ be a prime split completely in $F$, and let $\overline{\rho}:G_F\longrightarrow {\rm GSp}_4(\overline{\mathbb{F}}_p)$ be a mod $p$ irreduci…