Lemma 67.38.8 (06CQ)—The Stacks project

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Part 4: Algebraic Spaces
Chapter 67: Morphisms of Algebraic Spaces
Section 67.38: Unramified morphisms
Lemma 67.38.8 (cite)

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Lemma 67.38.8. An immersion of algebraic spaces is unramified.

Proof. Let $i : X \to Y$ be an immersion of algebraic spaces. Choose a scheme $V$ and a surjective étale morphism $V \to Y$ . Then $V \times _ Y X \to V$ is an immersion of schemes, hence unramified (see Morphisms, Lemmas 29.35.7 and 29.35.8). Thus by definition $i$ is unramified. $\square$

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