Lemma 30.2.4. Let f : X \to S be an affine morphism of schemes. Let \mathcal{F} be a quasi-coherent \mathcal{O}_ X-module. Then H^ i(X, \mathcal{F}) = H^ i(S, f_*\mathcal{F}) for all i \geq 0.
Proof. Follows from Lemma 30.2.3 and the Leray spectral sequence. See Cohomology, Lemma 20.13.6. \square
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