Remark 75.17.4 (Variant with support). Let $S$ be a scheme. Let $X$ be a quasi-compact and quasi-separated algebraic space. Let $T \subset |X|$ be a closed subset such that $|X| \setminus T$ is quasi-compact. The analogue of Theorem 75.17.3 holds for $D_{\mathit{QCoh}, T}(\mathcal{O}_ X)$. This follows from the exact same argument as in the proof of the theorem, using Lemmas 75.15.6 and 75.16.3 and a variant of Lemma 75.17.1 with supports. If we ever need this, we will precisely state the result here and give a detailed proof.
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