Lemma 37.59.11. Let $X \to S$ be a morphism of schemes which is locally of finite type. Let $\mathcal{F}$ be an $\mathcal{O}_ X$-module. Then

$\mathcal{F}$ is $m$-pseudo-coherent relative to $S$ for all $m > 0$,

$\mathcal{F}$ is $0$-pseudo-coherent relative to $S$ if and only if $\mathcal{F}$ is a finite type $\mathcal{O}_ X$-module,

$\mathcal{F}$ is $(-1)$-pseudo-coherent relative to $S$ if and only if $\mathcal{F}$ is quasi-coherent and finitely presented relative to $S$.

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