Loading [MathJax]/extensions/tex2jax.js

The Stacks project

Lemma 10.158.6. Let $K/k$ be an extension of fields. Then $K$ is formally smooth over $k$ if and only if $H_1(L_{K/k}) = 0$.

Proof. This follows from Proposition 10.138.8 and the fact that a vector spaces is free (hence projective). $\square$


Comments (0)

There are also:

  • 2 comment(s) on Section 10.158: Formal smoothness of fields

Your email address will not be published.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.