Lemma 36.30.4. Let $S$ be a scheme. Let $f : X \to S$ be a proper morphism of finite presentation.

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

## Comments (2)

Comment #4352 by Remy on

Comment #4499 by Johan on