Lemma 46.7.1 (06ZQ)—The Stacks project

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Table of contents
Part 3: Topics in Scheme Theory
Chapter 46: Adequate Modules
Section 46.7: Derived categories of adequate modules, I
Lemma 46.7.1 (cite)

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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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