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

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

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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