Lemma 74.19.12. Let $S$ be a scheme. Let $f : X \to Y$, $g : Y \to Z$ be morphisms of algebraic spaces over $S$. Assume $f$ is formally smooth. Then

$0 \to f^*\Omega _{Y/Z} \to \Omega _{X/Z} \to \Omega _{X/Y} \to 0$

Lemma 74.7.8 is short exact.

Proof. Follows from the case of schemes, see More on Morphisms, Lemma 37.11.11, by étale localization, see Lemmas 74.19.10 and 74.7.3. $\square$

Comment #5140 by bouthier on

There is a typo in the short exact sequence. Last term should be $\Omega^{1}_{X/Y}$.

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