Lemma 70.3.5. 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. $\square$

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).