Lemma 31.6.5 (0CUC)—The Stacks project

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Table of contents
Part 2: Schemes
Chapter 31: Divisors
Section 31.6: Morphisms and weakly associated points
Lemma 31.6.5 (cite)

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Lemma 31.6.5. Let $K/k$ be a field extension. Let $X$ be a scheme 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 Algebra, Lemma 10.66.19 into the language of schemes. $\square$

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