“Geometric quotients are algebraic schemes” based on Fogarty’s idea
“Geometric quotients are algebraic schemes” based on Fogarty’s idea
Let $S$ be a Noetherian scheme, $\varphi : X \to Y$ a surjective $S$-morphism of $S$-schemes, with $X$ of finite type over $S$. We discuss what makes $Y$ of finite type. First, we prove that if $S$ is excellent, $Y$ is reduced, and $\varphi$ is universally open, then $Y$ is …