The Stacks project

Lemma 31.8.2. Let $f : X \to S$ be a morphism of schemes which is locally of finite type. Let $\mathcal{F}$ be a quasi-coherent $\mathcal{O}_ X$-module. Then $\text{WeakAss}_{X/S}(\mathcal{F}) = \text{Ass}_{X/S}(\mathcal{F})$.

Proof. This is true because the fibres of $f$ are locally Noetherian schemes, and associated and weakly associated points agree on locally Noetherian schemes, see Lemma 31.5.8. $\square$

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