2 problems

Let $A$ be an abelian variety over a number field $K$ with $K_A^{\operatorname{conn}}=K$. Let $\mathbf G_A$ be its Mumford–Tate group, let $\rho_{A,\ell}$ be the associated $ell$-a…

Let $X$ be a normal scheme of finite type over ${\mathbb{F}}_p$, let $\ell\ne p$ be a prime, and let $\mathcal{E}$ be an irreducible lisse $\overline{{\mathbb{Q}}}_{\ell}$-sheaf on…