Lemma 29.41.5. The base change of a proper morphism is proper. The same is true for universally closed morphisms.
Proof. This is true by definition for universally closed morphisms. It is true for separated morphisms (Schemes, Lemma 26.21.12). It is true for morphisms of finite type (Lemma 29.15.4). Hence it is true for proper morphisms. $\square$
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Your email address will not be published.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.