Definition 17.30.1. In the situation above, the *de Rham complex of $\mathcal{B}$ over $\mathcal{A}$* is the unique complex

of sheaves of $\mathcal{A}$-modules whose differential in degree $0$ is given by $\text{d} : \mathcal{B} \to \Omega _{\mathcal{B}/\mathcal{A}}$ and whose differentials in higher degrees have the following property

where $b_0, \ldots , b_ p \in \mathcal{B}(U)$ are sections over a common open $U \subset X$.

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