The Stacks project

Remark 66.7.3. Here is a list of properties which are local for the étale topology (keep in mind that the fpqc, fppf, syntomic, and smooth topologies are stronger than the étale topology):

  1. locally Noetherian, see Descent, Lemma 35.16.1,

  2. Jacobson, see Descent, Lemma 35.16.2,

  3. locally Noetherian and $(S_ k)$, see Descent, Lemma 35.17.1,

  4. Cohen-Macaulay, see Descent, Lemma 35.17.2,

  5. Gorenstein, see Duality for Schemes, Lemma 48.24.6,

  6. reduced, see Descent, Lemma 35.18.1,

  7. normal, see Descent, Lemma 35.18.2,

  8. locally Noetherian and $(R_ k)$, see Descent, Lemma 35.18.3,

  9. regular, see Descent, Lemma 35.18.4,

  10. Nagata, see Descent, Lemma 35.18.5.


Comments (0)


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Your email address will not be published.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 03E7. Beware of the difference between the letter 'O' and the digit '0'.