Lemma 28.42.10. A finite morphism is quasi-finite.
Proof. This is implied by Algebra, Lemma 10.121.4 and Lemma 28.19.9. Alternatively, all points in fibres are closed points by Lemma 28.42.8 (and the fact that a finite morphism is integral) and use Lemma 28.19.6 (3) to see that $f$ is quasi-finite at $x$ for all $x \in X$. $\square$
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Your email address will not be published.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.