Lemma 31.5.5 (05AP)—The Stacks project

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Table of contents
Part 2: Schemes
Chapter 31: Divisors
Section 31.5: Weakly associated points
Lemma 31.5.5 (cite)

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Lemma 31.5.5. Let $X$ be a scheme. Let $\mathcal{F}$ be a quasi-coherent $\mathcal{O}_ X$ -module. Then

$\mathcal{F} = (0) \Leftrightarrow \text{WeakAss}(\mathcal{F}) = \emptyset$

Proof. Follows from Lemma 31.5.2 and Algebra, Lemma 10.66.5 $\square$

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