The Stacks project

Lemma 71.3.5. Let $K/k$ be a field extension. Let $X$ be an algebraic space over $k$. Let $\mathcal{F}$ be a quasi-coherent $\mathcal{O}_ X$-module. Let $y \in X_ K$ with image $x \in X$. If $y$ is a weakly associated point of the pullback $\mathcal{F}_ K$, then $x$ is a weakly associated point of $\mathcal{F}$.

Proof. This is the translation of Divisors, Lemma 31.6.5 into the language of algebraic spaces. We omit the details of the translation. $\square$

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