Proposition 36.8.3. Let $X$ be a Noetherian scheme. Then the functor (36.3.0.1)

\[ D(\mathit{QCoh}(\mathcal{O}_ X)) \longrightarrow D_\mathit{QCoh}(\mathcal{O}_ X) \]

is an equivalence with quasi-inverse given by $RQ_ X$.

Proposition 36.8.3. Let $X$ be a Noetherian scheme. Then the functor (36.3.0.1)

\[ D(\mathit{QCoh}(\mathcal{O}_ X)) \longrightarrow D_\mathit{QCoh}(\mathcal{O}_ X) \]

is an equivalence with quasi-inverse given by $RQ_ X$.

**Proof.**
This follows from Lemma 36.7.4 and Lemma 36.8.2.
$\square$

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