2 problems

Let $K$ and $L$ be finitely generated infinite fields, let $\bar K$ and $\bar L$ be algebraic closures, and write $K^{\rm perf}$ and $L^{\rm perf}$ for their perfect closures. Let…

Let $K|k$ and $L|l$ be function fields over algebraically closed fields. Let $\mathcal{G}_K^a$ and $\mathcal{G}_L^a$ denote the mod-$\ell$ abelianized Galois groups, and let…