The Stacks project

Lemma 71.3.6. Let $S$ be a scheme. Let $f : X \to Y$ be a finite flat morphism of algebraic spaces. Let $\mathcal{G}$ be a quasi-coherent $\mathcal{O}_ Y$-module. Let $x \in |X|$ be a point with image $y \in |Y|$. Then

\[ x \in \text{WeakAss}(g^*\mathcal{G}) \Leftrightarrow y \in \text{WeakAss}(\mathcal{G}) \]

Proof. Follows immediately from the case of schemes (More on Flatness, Lemma 38.2.7) by étale localization. $\square$

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