The Stacks project

Definition 59.31.3. Let $S$ be a scheme. Let $\mathcal{F}$ be an abelian sheaf on $S_{\acute{e}tale}$.

  1. The support of $\mathcal{F}$ is the set of points $s \in S$ such that $\mathcal{F}_{\overline{s}} \not= 0$ for any (some) geometric point $\overline{s}$ lying over $s$.

  2. Let $\sigma \in \mathcal{F}(U)$ be a section. The support of $\sigma $ is the closed subset $U \setminus W$, where $W \subset U$ is the largest open subset of $U$ on which $\sigma $ restricts to zero (see Lemma 59.31.2).

Comments (0)

There are also:

  • 4 comment(s) on Section 59.31: Supports of abelian sheaves

Post a comment

Your email address will not be published. Required fields are marked.

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).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

All contributions are licensed under the GNU Free Documentation License.




In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling in the name of the current tag in the following input field. As a reminder, this is tag 04FS. Beware of the difference between the letter 'O' and the digit '0'.



View Definition 59.31.3 as pdf