Lemma 20.37.9. Let $(X, \mathcal{O}_ X)$ be a ringed space. Let $E \in D(\mathcal{O}_ X)$. Assume there exist an integer $d \geq 0$ and a basis $\mathcal{B}$ for the topology of $X$ such that

Then the map $E \to R\mathop{\mathrm{lim}}\nolimits \tau _{\geq -n} E$ of Derived Categories, Remark 13.34.4 is an isomorphism in $D(\mathcal{O}_ X)$.

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