Definition 29.32.1. Let $f : X \to S$ be a morphism of schemes. The *sheaf of differentials $\Omega _{X/S}$ of $X$ over $S$* is the sheaf of differentials of $f$ viewed as a morphism of ringed spaces (Modules, Definition 17.28.10) equipped with its *universal $S$-derivation*

\[ \text{d}_{X/S} : \mathcal{O}_ X \longrightarrow \Omega _{X/S}. \]

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