Lemma 31.4.3. Let $X$ be a locally Noetherian scheme. Let $\mathcal{F}$ be a coherent sheaf on $X$. Then the following are equivalent:

1. $\mathcal{F}$ has no embedded associated points, and

2. $\mathcal{F}$ has property $(S_1)$.

Proof. This is Algebra, Lemma 10.157.2, combined with Lemma 31.2.2 above. $\square$

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