Lemma 37.67.2. Let $X \to T \to S$ be morphisms of schemes. Assume $T \to S$ is flat and locally of finite presentation and $X \to T$ locally of finite type. Let $E \in D(\mathcal{O}_ X)$. Let $m \in \mathbf{Z}$. Then $E$ is $m$-pseudo-coherent relative to $S$ if and only if $E$ is $m$-pseudo-coherent relative to $T$.

**Proof.**
Locally on $X$ we can choose a closed immersion $i : X \to \mathbf{A}^ n_ T$. Then $\mathbf{A}^ n_ T \to S$ is flat and locally of finite presentation. Thus we may apply Lemma 37.56.17 to see the equivalence holds.
$\square$

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