Lemma 70.6.4. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. Let $D \subset X$ be an effective Cartier divisor. Let $U = X \setminus D$. Then $U \to X$ is an affine morphism and $U$ is scheme theoretically dense in $X$.
Proof. Affineness is Lemma 70.6.3. The density question is étale local on $X$ by Morphisms of Spaces, Definition 66.17.3. Thus this follows from the case of schemes which is Divisors, Lemma 31.13.4. $\square$
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Your email address will not be published.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).
All contributions are licensed under the GNU Free Documentation License.