Lemma 73.25.4. Let $S$ be a scheme. Let $f : X \to Y$ be a proper morphism of finite presentation of algebraic spaces over $S$.

Let $E \in D(\mathcal{O}_ X)$ be perfect and $f$ flat. Then $Rf_*E$ is a perfect object of $D(\mathcal{O}_ Y)$ and its formation commutes with arbitrary base change.

Let $\mathcal{G}$ be an $\mathcal{O}_ X$-module of finite presentation, flat over $S$. Then $Rf_*\mathcal{G}$ is a perfect object of $D(\mathcal{O}_ Y)$ and its formation commutes with arbitrary base change.

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