Lemma 20.45.2. Let $(X, \mathcal{O}_ X)$ be a ringed space. Let $E$ be an object of $D(\mathcal{O}_ X)$.

If there exists an open covering $X = \bigcup U_ i$, strictly perfect complexes $\mathcal{E}_ i^\bullet $ on $U_ i$, and maps $\alpha _ i : \mathcal{E}_ i^\bullet \to E|_{U_ i}$ in $D(\mathcal{O}_{U_ i})$ with $H^ j(\alpha _ i)$ an isomorphism for $j > m$ and $H^ m(\alpha _ i)$ surjective, then $E$ is $m$-pseudo-coherent.

If $E$ is $m$-pseudo-coherent, then any complex representing $E$ is $m$-pseudo-coherent.

## Comments (2)

Comment #2770 by Mahdi Majidi-Zolbanin on

Comment #2879 by Johan on