The Stacks project

Definition 21.43.1. In the situation above, we denote $\mathit{QC}(\mathcal{C}, \mathcal{O})$ or simply $\mathit{QC}(\mathcal{O})$ the full subcategory of $D(\mathcal{O}) = D(\mathcal{C}, \mathcal{O})$ consisting of objects $K$ such that for all $U \to V$ in $\mathcal{C}$ the canonical map

\[ R\Gamma (V, K) \otimes _{\mathcal{O}(V)}^\mathbf {L} \mathcal{O}(U) \longrightarrow R\Gamma (U, K) \]

is an isomorphism in $D(\mathcal{O}(U))$.

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View Definition 21.43.1 as pdf