The Stacks project

Proposition 75.12.6. Let $S$ be a scheme. Let $X$ be a Noetherian algebraic space over $S$. Then the functor (75.5.1.1)

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

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

Proof. Follows immediately from Lemmas 75.12.5 and 75.11.4. $\square$

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