Definition 15.62.1. Let $R$ be a ring. Denote $D(R)$ its derived category. Let $m \in \mathbf{Z}$.

An object $K^\bullet $ of $D(R)$ is

*$m$-pseudo-coherent*if there exists a bounded complex $E^\bullet $ of finite free $R$-modules and a morphism $\alpha : E^\bullet \to K^\bullet $ such that $H^ i(\alpha )$ is an isomorphism for $i > m$ and $H^ m(\alpha )$ is surjective.An object $K^\bullet $ of $D(R)$ is

*pseudo-coherent*if it is quasi-isomorphic to a bounded above complex of finite free $R$-modules.An $R$-module $M$ is called

*$m$-pseudo-coherent*if $M[0]$ is an $m$-pseudo-coherent object of $D(R)$.An $R$-module $M$ is called

*pseudo-coherent*^{1}if $M[0]$ is a pseudo-coherent object of $D(R)$.

## Comments (1)

Comment #160 by Pieter Belmans on