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The Stacks project

Lemma 50.3.1. Let X \to S be a morphism of affine schemes given by the ring map R \to A. Then R\Gamma (X, \Omega ^\bullet _{X/S}) = \Omega ^\bullet _{A/R} in D(R) and H^ i_{dR}(X/S) = H^ i(\Omega ^\bullet _{A/R}).

Proof. This follows from Cohomology of Schemes, Lemma 30.2.2 and Leray's acyclicity lemma (Derived Categories, Lemma 13.16.7). \square


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