The Stacks project

Definition 52.6.4. Let $(\mathcal{C}, \mathcal{O})$ be a ringed site. Let $\mathcal{I} \subset \mathcal{O}$ be a sheaf of ideals. Let $K \in D(\mathcal{O})$. We say that $K$ is derived complete with respect to $\mathcal{I}$ if for every object $U$ of $\mathcal{C}$ and $f \in \mathcal{I}(U)$ the object $T(K|_ U, f)$ of $D(\mathcal{O}_ U)$ is zero.