Lemma 20.45.10. Let $(X, \mathcal{O}_ X)$ be a ringed space. Let $\mathcal{F}$ be a sheaf of $\mathcal{O}_ X$-modules.

$\mathcal{F}$ viewed as an object of $D(\mathcal{O}_ X)$ is $0$-pseudo-coherent if and only if $\mathcal{F}$ is a finite type $\mathcal{O}_ X$-module, and

$\mathcal{F}$ viewed as an object of $D(\mathcal{O}_ X)$ is $(-1)$-pseudo-coherent if and only if $\mathcal{F}$ is an $\mathcal{O}_ X$-module of finite presentation.

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