Lemma 75.25.5. Let $S$ be a scheme. Let $f : X \to Y$ be a flat proper morphism of finite presentation of algebraic spaces over $S$. Let $E \in D(\mathcal{O}_ X)$ be pseudo-coherent. Then $Rf_*E$ is a pseudo-coherent object of $D(\mathcal{O}_ Y)$ and its formation commutes with arbitrary base change.

**Proof.**
Special case of Lemma 75.25.3 applied with $\mathcal{G} = \mathcal{O}_ X$.
$\square$

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