The Stacks project

Lemma 28.7.7. Let $X$ be a locally Noetherian scheme. The following are equivalent:

  1. $X$ is normal, and

  2. $X$ is a disjoint union of integral normal schemes.

Proof. Omitted. Hint: This is purely topological from Lemma 28.7.6. $\square$


Comments (2)

Comment #276 by BB on

Maybe I'm missing some definition, but probably "normal" should not be an assumption on the locally noetherian scheme X in the statement.

There are also:

  • 4 comment(s) on Section 28.7: Normal 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Your email address will not be published.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 033N. Beware of the difference between the letter 'O' and the digit '0'.