The Stacks project

Lemma 72.8.4. Let $S$ be a scheme. Let $f : X \to Y$ be a proper dominant morphism of integral algebraic spaces over $S$. Then $f$ is an alteration if and only if any of the equivalent conditions (1) – (6) of Lemma 72.5.1 hold.

Proof. Immediate consequence of the lemma referenced in the statement. $\square$

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