Lemma 100.37.4. A closed immersion of algebraic stacks is a proper morphism of algebraic stacks.
Proof. A closed immersion is by definition representable (Properties of Stacks, Definition 99.9.1). Hence this follows from the discussion in Properties of Stacks, Section 99.3 and the corresponding result for morphisms of algebraic spaces, see Morphisms of Spaces, Lemma 66.40.5. $\square$
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Your email address will not be published.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.