Remark 75.16.2. Let $S$ be a scheme. Let $X$ be a quasi-compact and quasi-separated algebraic space over $S$. Let $G$ be a perfect object of $D(\mathcal{O}_ X)$ which is a generator for $D_\mathit{QCoh}(\mathcal{O}_ X)$. By Theorem 75.15.4 there is at least one of these. Combining Lemma 75.5.3 with Proposition 75.16.1 and with Derived Categories, Proposition 13.37.6 we see that $G$ is a classical generator for $D_{perf}(\mathcal{O}_ X)$.
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Your email address will not be published.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)