Lemma 36.15.1. Let $X$ be a quasi-compact and quasi-separated scheme. Let $U$ be a quasi-compact open subscheme. Let $P$ be a perfect object of $D(\mathcal{O}_ U)$. Then $P$ is a direct summand of the restriction of a perfect object of $D(\mathcal{O}_ X)$.

**Proof.**
Special case of Lemma 36.13.10.
$\square$

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