Definition 31.2.1. Let $X$ be a scheme. Let $\mathcal{F}$ be a quasi-coherent sheaf on $X$.

1. We say $x \in X$ is associated to $\mathcal{F}$ if the maximal ideal $\mathfrak m_ x$ is associated to the $\mathcal{O}_{X, x}$-module $\mathcal{F}_ x$.

2. We denote $\text{Ass}(\mathcal{F})$ or $\text{Ass}_ X(\mathcal{F})$ the set of associated points of $\mathcal{F}$.

3. The associated points of $X$ are the associated points of $\mathcal{O}_ X$.

There are also:

• 2 comment(s) on Section 31.2: Associated points

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).