The Stacks project

Lemma 29.35.5. The base change of a morphism which is unramified is unramified. The same holds for G-unramified morphisms.

Proof. The proof of Lemma 29.35.3 shows that being unramified (resp. G-unramified) is a local property of ring maps. Hence the lemma follows from Lemma 29.14.6 combined with the fact that being unramified (resp. G-unramified) is a property of ring maps that is stable under base change, see Algebra, Lemma 10.151.3. $\square$

Comments (2)

Comment #4627 by Shii on

typo(wrong link): "Hence the lemma follows from Lemma 28.13.5" -> "Hence the lemma follows from Lemma 28.13.6"

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Your email address will not be published.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 02GA. Beware of the difference between the letter 'O' and the digit '0'.



View Lemma 29.35.5 as pdf