Lemma 15.81.10. Let $R \to A$ be a finite type ring map. Let $m \in \mathbf{Z}$. Let $K^\bullet \in D^{-}(A)$ such that $H^ i(K^\bullet )$ is $(m - i)$-pseudo-coherent (resp. pseudo-coherent) relative to $R$ for all $i$. Then $K^\bullet$ is $m$-pseudo-coherent (resp. pseudo-coherent) relative to $R$.

Proof. Immediate from Lemma 15.64.10 and the definitions. $\square$

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