The Stacks project

Definition 96.7.1. Let $\mathcal{X}$ be a category fibred in groupoids over $(\mathit{Sch}/S)_{fppf}$.

  1. A presheaf of modules on $\mathcal{X}$ is a presheaf of $\mathcal{O}_\mathcal {X}$-modules. The category of presheaves of modules is denoted $\textit{PMod}(\mathcal{O}_\mathcal {X})$.

  2. We say a presheaf of modules $\mathcal{F}$ is an $\mathcal{O}_\mathcal {X}$-module, or more precisely a sheaf of $\mathcal{O}_\mathcal {X}$-modules if $\mathcal{F}$ is an fppf sheaf. The category of $\mathcal{O}_\mathcal {X}$-modules is denoted $\textit{Mod}(\mathcal{O}_\mathcal {X})$.

Comments (0)

There are also:

  • 2 comment(s) on Section 96.7: Sheaves of modules

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Your email address will not be published.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 06WB. Beware of the difference between the letter 'O' and the digit '0'.


View Definition 96.7.1 as pdf