The Stacks project

Lemma 76.7.12. Let $S$ be a scheme. Let $X \to Y$ be a morphism of algebraic spaces over $S$. Let $g : Y' \to Y$ be a morphism of algebraic spaces over $S$. Let $X' = X_{Y'}$ be the base change of $X$. Denote $g' : X' \to X$ the projection. Then the map

\[ (g')^*\Omega _{X/Y} \to \Omega _{X'/Y'} \]

of Lemma 76.7.6 is an isomorphism.

Proof. Follows from the schemes version, see Morphisms, Lemma 29.32.10 and étale localization, see Lemma 76.7.3. $\square$

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