Definition 17.29.4. Let $f : (X, \mathcal{O}_ X) \to (Y, \mathcal{O}_ Y)$ be a morphism of ringed spaces. The *de Rham complex* of $f$ or of $X$ over $Y$ is the complex

\[ \Omega ^\bullet _{X/Y} = \Omega ^\bullet _{\mathcal{O}_ X/f^{-1}\mathcal{O}_ Y} \]

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