Lemma 35.18.4. The property $\mathcal{P}(S) =$“$S$ is regular” is local in the smooth topology.

**Proof.**
This is clear from Lemma 35.18.3 above since a locally Noetherian scheme is regular if and only if it is locally Noetherian and $(R_ k)$ for all $k \geq 0$.
$\square$

## 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Your email address will not be published.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 (0)