Lemma 20.37.7. Let (X, \mathcal{O}_ X) be a ringed space. Let E \in D(\mathcal{O}_ X). Assume that for every x \in X there exist an integer d_ x \geq 0 and a fundamental system \mathfrak {U}_ x of open neighbourhoods 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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