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.
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