Lemma 68.12.1 (03K5)—The Stacks project

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Table of contents
Part 4: Algebraic Spaces
Chapter 68: Decent Algebraic Spaces
Section 68.12: Points on decent spaces
Lemma 68.12.1 (cite)

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Lemma 68.12.1. Let $S$ be a scheme. Let $X$ be a decent algebraic space over $S$ . Let $U \to X$ be an étale morphism from a scheme to $X$ . If $u, u' \in |U|$ map to the same point of $|X|$ , and $u' \leadsto u$ , then $u = u'$ .

Proof. Combine Lemmas 68.5.1 and 68.7.1. $\square$

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