Definition 75.14.1. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. Consider triples $(T, E, m)$ where

$T \subset |X|$ is a closed subset,

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

$m \in \mathbf{Z}$.

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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