Lemma 31.5.3 (05AM)—The Stacks project

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Table of contents
Part 2: Schemes
Chapter 31: Divisors
Section 31.5: Weakly associated points
Lemma 31.5.3 (cite)

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Lemma 31.5.3. Let $X$ be a scheme. Let $\mathcal{F}$ be a quasi-coherent $\mathcal{O}_ X$ -module. Then

$\text{Ass}(\mathcal{F}) \subset \text{WeakAss}(\mathcal{F}) \subset \text{Supp}(\mathcal{F}).$

Proof. This is immediate from the definitions. $\square$

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