The Stacks project

Definition 27.8.3. Let $S$ be a graded ring.

  1. The structure sheaf $\mathcal{O}_{\text{Proj}(S)}$ of the homogeneous spectrum of $S$ is the unique sheaf of rings $\mathcal{O}_{\text{Proj}(S)}$ which agrees with $\widetilde S$ on the basis of standard opens.

  2. The locally ringed space $(\text{Proj}(S), \mathcal{O}_{\text{Proj}(S)})$ is called the homogeneous spectrum of $S$ and denoted $\text{Proj}(S)$.

  3. The sheaf of $\mathcal{O}_{\text{Proj}(S)}$-modules extending $\widetilde M$ to all opens of $\text{Proj}(S)$ is called the sheaf of $\mathcal{O}_{\text{Proj}(S)}$-modules associated to $M$. This sheaf is denoted $\widetilde M$ as well.

Comments (0)

There are also:

  • 13 comment(s) on Section 27.8: Proj of a graded ring

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Your email address will not be published.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 01M6. Beware of the difference between the letter 'O' and the digit '0'.



View Definition 27.8.3 as pdf