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.

## 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Your email address will not be published.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.

## Comments (2)

Comment #2616 by Harry on

Comment #2636 by Johan on

There are also: