The Stacks project

Definition 74.7.2. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$. The sheaf of differentials $\Omega _{X/Y}$ of $X$ over $Y$ is sheaf of differentials (Modules on Sites, Definition 18.33.10) for the morphism of ringed topoi

\[ (f_{small}, f^\sharp ) : (X_{\acute{e}tale}, \mathcal{O}_ X) \to (Y_{\acute{e}tale}, \mathcal{O}_ Y) \]

of Properties of Spaces, Lemma 64.21.3. The universal $Y$-derivation will be denoted $\text{d}_{X/Y} : \mathcal{O}_ X \to \Omega _{X/Y}$.


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