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The Stacks project

Remark 36.17.4. Let X be a quasi-compact and quasi-separated scheme. 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 36.15.4 there is at least one of these. Combining the fact that D_{\mathit{QCoh}, T}(\mathcal{O}_ X) has direct sums with Lemma 36.17.3 and with Derived Categories, Proposition 13.37.6 we see that G is a classical generator for D_{perf, T}(\mathcal{O}_ X).


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