The Stacks project

60.14 The de Rham complex

In Situation 60.7.5. Working on the (small) crystalline site, we define $\Omega ^ i_{X/S} = \wedge ^ i_{\mathcal{O}_{X/S}} \Omega _{X/S}$ for $i \geq 0$. The universal $S$-derivation $\text{d}_{X/S}$ gives rise to the de Rham complex

\[ \mathcal{O}_{X/S} \to \Omega ^1_{X/S} \to \Omega ^2_{X/S} \to \ldots \]

on $\text{Cris}(X/S)$, see Lemma 60.12.4 and Remark 60.6.7.

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