The Stacks project

Remark 75.16.4. Let $S$ be a scheme. Let $X$ be a quasi-compact and quasi-separated algebraic space over $S$. Let $T \subset |X|$ be a closed subset such that $|X| \setminus T$ is quasi-compact. Let $G$ be a perfect object of $D_{\mathit{QCoh}, T}(\mathcal{O}_ X)$ which is a generator for $D_{\mathit{QCoh}, T}(\mathcal{O}_ X)$. By Lemma 75.15.6 there is at least one of these. Combining the fact that $D_{\mathit{QCoh}, T}(\mathcal{O}_ X)$ has direct sums with Lemma 75.16.3 and with Derived Categories, Proposition 13.37.6 we see that $G$ is a classical generator for $D_{perf, T}(\mathcal{O}_ X)$.