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. $\square$

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).