The Stacks project

Lemma 59.64.6. Let $X$ be a scheme.

  1. The category of finite locally constant sheaves of sets is closed under finite limits and colimits inside $\mathop{\mathit{Sh}}\nolimits (X_{\acute{e}tale})$.

  2. The category of finite locally constant abelian sheaves is a weak Serre subcategory of $\textit{Ab}(X_{\acute{e}tale})$.

  3. Let $\Lambda $ be a Noetherian ring. The category of finite type, locally constant sheaves of $\Lambda $-modules on $X_{\acute{e}tale}$ is a weak Serre subcategory of $\textit{Mod}(X_{\acute{e}tale}, \Lambda )$.

Proof. This holds on any site, see Modules on Sites, Lemma 18.43.5. $\square$

Comments (0)

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Your email address will not be published.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 03RX. Beware of the difference between the letter 'O' and the digit '0'.