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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