Lemma 67.39.12. A locally finitely presented, flat, unramified morphism of algebraic spaces is étale.
Proof. Let X \to Y be a locally finitely presented, flat, unramified morphism of algebraic spaces. By Properties of Spaces, Lemma 66.16.3 we see this means there exists a diagram as in Lemma 67.22.1 with h locally finitely presented, flat, unramified and surjective vertical arrow a. By Morphisms, Lemma 29.36.16 h is étale. Hence X \to Y is étale by definition. \square
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