Lemma 60.12.2. Let $(T, \mathcal{J}, \delta )$ be a divided power scheme. Let $T \to S$ be a morphism of schemes. The quotient $\Omega _{T/S} \to \Omega _{T/S, \delta }$ described above is a quasi-coherent $\mathcal{O}_ T$-module. For $W \subset T$ affine open mapping into $V \subset S$ affine open we have

$\Gamma (W, \Omega _{T/S, \delta }) = \Omega _{\Gamma (W, \mathcal{O}_ W)/\Gamma (V, \mathcal{O}_ V), \delta }$

where the right hand side is as constructed in Section 60.6.

Proof. Omitted. $\square$

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