Definition 29.32.1 (01UQ)—The Stacks project

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Table of contents
Part 2: Schemes
Chapter 29: Morphisms of Schemes
Section 29.32: Sheaf of differentials of a morphism
Definition 29.32.1 (cite)

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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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