The Stacks project

Lemma 46.7.1. Let $S$ be a scheme. Let $\mathcal{C} \subset \textit{Adeq}(\mathcal{O})$ denote the full subcategory consisting of parasitic adequate modules. Then

\[ D(\textit{Adeq}(\mathcal{O}))/D_\mathcal {C}(\textit{Adeq}(\mathcal{O})) = D(\mathit{QCoh}(\mathcal{O}_ S)) \]

and similarly for the bounded versions.

Proof. Follows immediately from Derived Categories, Lemma 13.17.3. $\square$

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