Lemma 75.15.3 (09IX)—The Stacks project

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Table of contents
Part 4: Algebraic Spaces
Chapter 75: Derived Categories of Spaces
Section 75.15: Generating derived categories
Lemma 75.15.3 (cite)

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Lemma 75.15.3. Let $S$ be a scheme. Let $X$ be a quasi-compact and quasi-separated algebraic space over $S$ . Let $W$ be a quasi-compact open subspace of $X$ . Let $P$ be a perfect object of $D(\mathcal{O}_ W)$ . Then $P$ is a direct summand of the restriction of a perfect object of $D(\mathcal{O}_ X)$ .

Proof. Special case of Lemma 75.15.1. $\square$

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