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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