Definition 17.30.1. In the situation above, the de Rham complex of \mathcal{B} over \mathcal{A} is the unique complex
\Omega _{\mathcal{B}/\mathcal{A}}^0 \to \Omega _{\mathcal{B}/\mathcal{A}}^1 \to \Omega _{\mathcal{B}/\mathcal{A}}^2 \to \ldots
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
17.30.1.1
\begin{equation} \label{modules-equation-rule} \text{d}\left(b_0\text{d}b_1 \wedge \ldots \wedge \text{d}b_ p\right) = \text{d}b_0 \wedge \text{d}b_1 \wedge \ldots \wedge \text{d}b_ p \end{equation}
where b_0, \ldots , b_ p \in \mathcal{B}(U) are sections over a common open U \subset X.
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