Lemma 74.19.1. The property $\mathcal{P}(f)=$“$f$ is étale” is étale local on the source.
74.19 Properties of morphisms local in the étale topology on the source
Here are some properties of morphisms that are étale local on the source.
Proof. Follows from Lemma 74.14.3 using Morphisms of Spaces, Definition 67.39.1 and Descent, Lemma 35.31.1. $\square$
Lemma 74.19.2. The property $\mathcal{P}(f)=$“$f$ is locally quasi-finite” is étale local on the source.
Proof. Follows from Lemma 74.14.3 using Morphisms of Spaces, Definition 67.27.1 and Descent, Lemma 35.31.2. $\square$
Lemma 74.19.3. The property $\mathcal{P}(f)=$“$f$ is unramified” is étale local on the source.
Proof. Follows from Lemma 74.14.3 using Morphisms of Spaces, Definition 67.38.1 and Descent, Lemma 35.31.3. $\square$
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Your email address will not be published.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).
All contributions are licensed under the GNU Free Documentation License.
Comments (0)