Lemma 31.4.2. Let $X$ be a locally Noetherian scheme. Let $\mathcal{F}$ be a coherent $\mathcal{O}_ X$-module. Then

the generic points of irreducible components of $\text{Supp}(\mathcal{F})$ are associated points of $\mathcal{F}$, and

an associated point of $\mathcal{F}$ is embedded if and only if it is not a generic point of an irreducible component of $\text{Supp}(\mathcal{F})$.

In particular an embedded point of $X$ is an associated point of $X$ which is not a generic point of an irreducible component of $X$.

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