The Stacks project

Definition 26.12.5. Let $X$ be a scheme. Let $Z \subset X$ be a closed subset. A scheme structure on $Z$ is given by a closed subscheme $Z'$ of $X$ whose underlying set is equal to $Z$. We often say “let $(Z, \mathcal{O}_ Z)$ be a scheme structure on $Z$” to indicate this. The reduced induced scheme structure on $Z$ is the one constructed in Lemma 26.12.4. The reduction $X_{red}$ of $X$ is the reduced induced scheme structure on $X$ itself.

Comments (2)

Comment #2616 by Harry on

I guess "underlying closed" should be "underlying set". Another cosmetic suggestion: Change the second sentence to "Let be a closed subset.", which is the form that's used in the subsequent paragraphs.

There are also:

  • 2 comment(s) on Section 26.12: Reduced schemes

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Your email address will not be published.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 01J4. Beware of the difference between the letter 'O' and the digit '0'.



View Definition 26.12.5 as pdf