The Stacks project

Lemma 74.7.8. Let $S$ be a scheme. Let $f : X \to Y$, $g : Y \to B$ be morphisms of algebraic spaces over $S$. Then there is a canonical exact sequence

\[ f^*\Omega _{Y/B} \to \Omega _{X/B} \to \Omega _{X/Y} \to 0 \]

where the maps come from applications of Lemma 74.7.6.

Proof. Follows from the schemes version, see Morphisms, Lemma 29.32.9, of this result via ├ętale localization, see Lemma 74.7.3. $\square$


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