Lemma 37.56.14. Let $X \to S$ be a morphism of schemes which is locally of finite type. Let $m \in \mathbf{Z}$. Let $E$ be an object of $D(\mathcal{O}_ X)$. If $E$ is (locally) bounded above and $H^ i(E)$ is $(m - i)$-pseudo-coherent relative to $S$ for all $i$, then $E$ is $m$-pseudo-coherent relative to $S$.

**Proof.**
Follows from Cohomology, Lemma 20.44.8 and the definitions.
$\square$

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