Lemma 36.7.3. Let $X = \mathop{\mathrm{Spec}}(A)$ be an affine scheme. Then

$Q_ X : \textit{Mod}(\mathcal{O}_ X) \to \mathit{QCoh}(\mathcal{O}_ X)$ is the functor which sends $\mathcal{F}$ to the quasi-coherent $\mathcal{O}_ X$-module associated to the $A$-module $\Gamma (X, \mathcal{F})$,

$RQ_ X : D(\mathcal{O}_ X) \to D(\mathit{QCoh}(\mathcal{O}_ X))$ is the functor which sends $E$ to the complex of quasi-coherent $\mathcal{O}_ X$-modules associated to the object $R\Gamma (X, E)$ of $D(A)$,

restricted to $D_\mathit{QCoh}(\mathcal{O}_ X)$ the functor $RQ_ X$ defines a quasi-inverse to (36.3.0.1).

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