Lemma 41.11.5. Let $Y$ be a locally Noetherian scheme. Let $f : X \to Y$ be locally of finite type. Let $x \in X$. The morphism $f$ is étale at $x$ in the sense of Definition 41.11.4 if and only if it is étale at $x$ in the sense of Morphisms, Definition 29.36.1.

**Proof.**
This follows from Lemma 41.11.2 and the definitions.
$\square$

## 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Your email address will not be published.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: