Lemma 72.8.4 (0ADB)—The Stacks project

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Table of contents
Part 4: Algebraic Spaces
Chapter 72: Algebraic Spaces over Fields
Section 72.8: Modifications and alterations
Lemma 72.8.4 (cite)

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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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