Lemma 76.7.16 (0CK5)—The Stacks project

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Table of contents
Part 4: Algebraic Spaces
Chapter 76: More on Morphisms of Spaces
Section 76.7: Sheaf of differentials of a morphism
Lemma 76.7.16 (cite)

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Lemma 76.7.16. Let $S$ be a scheme. Let $f : X \to Y$ be a smooth morphism of algebraic spaces over $S$ . Then the module of differentials $\Omega _{X/Y}$ is finite locally free.

Proof. The statement is étale local on $X$ and $Y$ by Lemma 76.7.3. Hence this follows from the case of schemes, see Morphisms, Lemma 29.34.12. $\square$

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