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The Stacks project

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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