The Stacks project

Lemma 21.47.5. Let $(f, f^\sharp ) : (\mathcal{C}, \mathcal{O}_\mathcal {C}) \to (\mathcal{D}, \mathcal{O}_\mathcal {D})$ be a morphism of ringed sites. Let $E$ be an object of $D(\mathcal{O}_\mathcal {D})$. If $E$ is perfect in $D(\mathcal{O}_\mathcal {D})$, then $Lf^*E$ is perfect in $D(\mathcal{O}_\mathcal {C})$.

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