Definition 70.8.3. 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 $U \subset X$.

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