Lemma 71.6.3. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. Let $Z \subset X$ be a locally principal closed subspace. Let $U = X \setminus Z$. Then $U \to X$ is an affine morphism.

**Proof.**
The question is étale local on $X$, see Morphisms of Spaces, Lemmas 67.20.3 and Lemma 71.6.2. Thus this follows from the case of schemes which is Divisors, Lemma 31.13.3.
$\square$

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Your email address will not be published.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

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)