4 problems

Let $A$ be the coordinate ring of the affine curve under consideration, and let $pi_1(A)$ denote its algebraic fundamental group. Harbater's conjecture. The algebraic fundamental g…

Let $(X/Z,B)$ be a log pair and let $\pi(X/Z)$ be its local or global algebraic fundamental group. A trivial complement is a complement with unchanged boundary, $B^+=B$; such compl…

Let $K={\bf F}_q(T)$, let $G/K$ be an isotropic, semisimple, simply-connected algebraic group, and let $Z$ be its center. Let ${\bf A}^{\mathrm{fin}}_K$ denote the finite adeles of…

Assume that $\operatorname{char}(k)\neq 2$, that $\pi:\widetilde X\rightarrow X$ is a possibly ramified double cover with involution $\sigma$, and set…