Lemma 36.30.5 (0CSD)—The Stacks project

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Table of contents
Part 2: Schemes
Chapter 36: Derived Categories of Schemes
Section 36.30: Cohomology and base change, VI
Lemma 36.30.5 (cite)

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Lemma 36.30.5. Let $S$ be a scheme. Let $f : X \to S$ be a flat proper morphism of finite presentation. Let $E \in D(\mathcal{O}_ X)$ be pseudo-coherent. Then $Rf_*E$ is a pseudo-coherent object of $D(\mathcal{O}_ S)$ and its formation commutes with arbitrary base change.

Proof. Special case of Lemma 36.30.3 applied with $\mathcal{G}^\bullet$ equal to $\mathcal{O}_ X$ in degree $0$ . $\square$

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