The Stacks project

Lemma 61.12.3. Any étale covering and any Zariski covering is a pro-étale covering.

Proof. This follows from the corresponding result for fpqc coverings (Topologies, Lemma 34.9.6), Lemma 61.12.2, and the fact that an étale morphism is a weakly étale morphism, see More on Morphisms, Lemma 37.62.9. $\square$

Comments (0)

There are also:

  • 6 comment(s) on Section 61.12: The pro-étale site

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Your email address will not be published.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.

In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling in the name of the current tag in the following input field. As a reminder, this is tag 098B. Beware of the difference between the letter 'O' and the digit '0'.