The Stacks project

Definition 72.8.3. Let $S$ be a scheme. Let $X$ be an integral algebraic space over $S$. An alteration of $X$ is a proper dominant morphism $f : Y \to X$ of algebraic spaces over $S$ with $Y$ integral such that $f^{-1}(U) \to U$ is finite for some nonempty open $U \subset X$.