Lemma 15.63.18. Let $R$ be a Noetherian ring. Then

A complex of $R$-modules $K^\bullet $ is $m$-pseudo-coherent if and only if $K^\bullet \in D^{-}(R)$ and $H^ i(K^\bullet )$ is a finite $R$-module for $i \geq m$.

A complex of $R$-modules $K^\bullet $ is pseudo-coherent if and only if $K^\bullet \in D^{-}(R)$ and $H^ i(K^\bullet )$ is a finite $R$-module for all $i$.

An $R$-module is pseudo-coherent if and only if it is finite.

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