Lemma 73.11.3. Let $S$ be a scheme. Let $X$ be an affine algebraic space over $S$. Set $A = \Gamma (X, \mathcal{O}_ X)$. 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 (73.5.1.1).

## Comments (1)

Comment #1652 by Pieter Belmans on