Lemma 35.29.1. The property $\mathcal{P}(f)=$“$f$ is smooth” is smooth local on the source.

Proof. Combine Lemma 35.25.4 with Morphisms, Lemma 29.34.2 (local for Zariski on source and target), Morphisms, Lemma 29.34.4 (pre-composing), and Lemma 35.13.4 (part (4)). $\square$

There are also:

• 2 comment(s) on Section 35.29: Properties of morphisms local in the smooth topology on the source

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).