The Stacks project

Definition 75.14.2. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. We say approximation by perfect complexes holds on $X$ if for any closed subset $T \subset |X|$ such that the morphism $X \setminus T \to X$ is quasi-compact there exists an integer $r$ such that for every triple $(T, E, m)$ as in Definition 75.14.1 with

  1. $E$ is $(m - r)$-pseudo-coherent, and

  2. $H^ i(E)$ is supported on $T$ for $i \geq m - r$

approximation holds.

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View Definition 75.14.2 as pdf