3 problems

Let $T_1\to T_2$ be a localized intrinsic étale morphism of strongly sheafy adic spaces. Local structure conjecture. Any localized intrinsic étale morphism of strongly sheafy adic…

Let $X$ be a smooth algebraic variety and let $q:U\to X$ be its universal covering, where $U$ need not be an algebraic variety. Universal-covering conjecture. The variety $X$ has a…

Let $X$ be a smooth algebraic variety over an algebraically closed field $k$ of characteristic zero, and let $\varphi:X\to X$ be an étale endomorphism. Generalized Jacobian conject…