Example 67.18.1. If $X, Y, Z$ are schemes, then the set $F_{x, z}$ is equal to the spectrum of $\kappa (x) \otimes _{\kappa (y)} \kappa (z)$ (Schemes, Lemma 26.17.5). Thus we obtain a finite set if either $\kappa (y) \subset \kappa (x)$ is finite or if $\kappa (y) \subset \kappa (z)$ is finite. In particular, this is always the case if $g$ is quasi-finite at $z$ (Morphisms, Lemma 29.20.5).

## 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Your email address will not be published.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)