Lemma 36.35.13. Let $f : X \to S$ be a morphism of schemes which is flat and locally of finite presentation. Let $E$ be a pseudo-coherent object of $D(\mathcal{O}_ X)$. The following are equivalent

$E$ is $S$-perfect, and

$E$ is locally bounded below and for every point $s \in S$ the object $L(X_ s \to X)^*E$ of $D(\mathcal{O}_{X_ s})$ is locally bounded below.

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