Lemma 29.33.5. The base change of a morphism which is smooth is smooth.
Proof. In the proof of Lemma 29.33.2 we saw that being smooth is a local property of ring maps. Hence the lemma follows from Lemma 29.14.5 combined with the fact that being smooth is a property of ring maps that is stable under base change, see Algebra, Lemma 10.136.4. $\square$
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Your email address will not be published.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).
All contributions are licensed under the GNU Free Documentation License.