Definition 77.19.3. In the situation of Definition 77.19.1. We say that the pre-relation $j$ has a quotient representable by an algebraic space if the sheaf $U/R$ is an algebraic space. We say that the pre-relation $j$ has a representable quotient if the sheaf $U/R$ is representable by a scheme. We will say a groupoid in algebraic spaces $(U, R, s, t, c)$ over $B$ has a representable quotient (resp. quotient representable by an algebraic space if the quotient $U/R$ with $j = (t, s)$ is representable (resp. an algebraic space).
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Your email address will not be published.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.