Lemma 37.59.13. Let $X \to S$ be a morphism of schemes which is locally of finite type. Let $m \in \mathbf{Z}$. Let $\mathcal{F}^\bullet $ be a (locally) bounded above complex of $\mathcal{O}_ X$-modules such that $\mathcal{F}^ i$ is $(m - i)$-pseudo-coherent relative to $S$ for all $i$. Then $\mathcal{F}^\bullet $ is $m$-pseudo-coherent relative to $S$.
Proof. Follows from Cohomology, Lemma 20.47.7 and the definitions. $\square$
Post a comment
Your email address will not be published. Required fields are marked.
In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).
All contributions are licensed under the GNU Free Documentation License.
Comments (0)