2 problems

Let $X$ be a smooth connected $p$-adic formal scheme over $\mathcal{O}_K$, let ${\mathrm{Spa}}(L)$ be the Shilov point of $X_\eta$, and let $T$ be a $\mathbb{Z}_p$-local system ove…

Let $F$ be a number field, let $X$ be a smooth variety over $F$, and let ${\mathbb L}$ be an irreducible $\overline{\mathbb{Q}}_p$-local system on $X$. Assume that there is a finit…