Lemma 66.51.1. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$. If $f$ is locally quasi-finite and separated, then $f$ is representable.

**Proof.**
This is immediate from Proposition 66.50.2 and the fact that being locally quasi-finite and separated is preserved under any base change, see Lemmas 66.27.4 and 66.4.4.
$\square$

## 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Your email address will not be published.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).

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 (2)

Comment #790 by Kestutis Cesnavicius on

Comment #801 by Johan on