The Stacks project

Lemma 70.6.10. Notation and assumptions as in Situation 70.6.1. If

  1. $f$ is a isomorphism,

  2. $f_0$ is locally of finite presentation,

then $f_ i$ is a isomorphism for some $i \geq 0$.

Proof. Being an isomorphism is equivalent to being étale, universally injective, and surjective, see Morphisms of Spaces, Lemma 67.51.2. Thus the lemma follows from Lemmas 70.6.2, 70.6.4, and 70.6.5. $\square$

Comments (0)

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Your email address will not be published.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 0852. Beware of the difference between the letter 'O' and the digit '0'.



View Lemma 70.6.10 as pdf