The Stacks project

Remark 74.21.5. Using Lemma 74.21.4 and the work done in the earlier sections of this chapter it is easy to make a list of types of morphisms which are smooth local on the source-and-target. In each case we list the lemma which implies the property is etale local on the source and the lemma which implies the property is smooth local on the target. In each case the third assumption of Lemma 74.21.4 is trivial to check, and we omit it. Here is the list:

  1. ├ętale, see Lemmas 74.19.1 and 74.11.28,

  2. locally quasi-finite, see Lemmas 74.19.2 and 74.11.24,

  3. unramified, see Lemmas 74.19.3 and 74.11.27, and

  4. add more here as needed.

Of course any property listed in Remark 74.20.5 is a fortiori an example that could be listed here.


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Your email address will not be published.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 0CG3. Beware of the difference between the letter 'O' and the digit '0'.