Lemma 67.37.7. A smooth morphism of algebraic spaces is flat.

**Proof.**
Let $X \to Y$ be a smooth morphism of algebraic spaces. By definition this means there exists a diagram as in Lemma 67.22.1 with $h$ smooth and surjective vertical arrow $a$. By Morphisms, Lemma 29.34.8 $h$ is flat. Hence $X \to Y$ is flat by definition.
$\square$

## 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Your email address will not be published.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)

There are also: