The Stacks project

Definition 36.14.1. Let $X$ be a scheme. Consider triples $(T, E, m)$ where

  1. $T \subset X$ is a closed subset,

  2. $E$ is an object of $D_\mathit{QCoh}(\mathcal{O}_ X)$, and

  3. $m \in \mathbf{Z}$.

We say approximation holds for the triple $(T, E, m)$ if there exists a perfect object $P$ of $D(\mathcal{O}_ X)$ supported on $T$ and a map $\alpha : P \to E$ which induces isomorphisms $H^ i(P) \to H^ i(E)$ for $i > m$ and a surjection $H^ m(P) \to H^ m(E)$.

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View Definition 36.14.1 as pdf