Lemma 70.2.3. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. Let $\mathcal{F}$ be a quasi-coherent $\mathcal{O}_ X$-module. Then $\text{WeakAss}(\mathcal{F}) \subset \text{Supp}(\mathcal{F})$.

**Proof.**
This is immediate from the definitions. The support of an abelian sheaf on $X$ is defined in Properties of Spaces, Definition 65.20.3.
$\square$

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