The Stacks project

Remark 36.17.2. Let $X$ be a quasi-compact and quasi-separated scheme. Let $G$ be a perfect object of $D(\mathcal{O}_ X)$ which is a generator for $D_\mathit{QCoh}(\mathcal{O}_ X)$. By Theorem 36.15.3 there is at least one of these. Combining Lemma 36.3.1 with Proposition 36.17.1 and with Derived Categories, Proposition 13.37.6 we see that $G$ is a classical generator for $D_{perf}(\mathcal{O}_ X)$.