The Stacks project

Remark 76.45.1. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of representable algebraic spaces over $S$ which is locally of finite type. Let $f_0 : X_0 \to Y_0$ be a morphism of schemes representing $f$ (awkward but temporary notation). Then $f_0$ is locally of finite type. If $E$ is an object of $D_\mathit{QCoh}(\mathcal{O}_ X)$, then $E$ is the pullback of a unique object $E_0$ in $D_\mathit{QCoh}(\mathcal{O}_{X_0})$, see Derived Categories of Spaces, Lemma 75.4.2. In this situation the phrase “$E$ is $m$-pseudo-coherent relative to $Y$” will be taken to mean “$E_0$ is $m$-pseudo-coherent relative to $Y_0$” as defined in More on Morphisms, Section 37.59.