Lemma 74.45.4. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$. Let $E$ in $D_\mathit{QCoh}(\mathcal{O}_ X)$. If $f$ is flat and locally of finite presentation, then the following are equivalent

1. $E$ is pseudo-coherent relative to $Y$, and

2. $E$ is pseudo-coherent on $X$.

Proof. By étale localization and the definitions we may assume $X$ and $Y$ are schemes. For the case of schemes this follows from More on Morphisms, Lemma 37.52.18. $\square$

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).