Lemma 39.18.4 (04ML)—The Stacks project

Processing math: 100%

Table of contents
Part 2: Schemes
Chapter 39: Groupoid Schemes
Section 39.18: Restricting groupoids
Lemma 39.18.4 (cite)

previous lemma

numberstags

history
statistics
1 tag refers to this tag

Lemma 39.18.4. Let $S$ be a scheme. Let $(U, R, s, t, c)$ be a groupoid scheme over $S$ . Let $g : U' \to U$ be a morphism of schemes. Let $(U', R', s', t', c')$ be the restriction of $(U, R, s, t, c)$ via $g$ . Let $G$ be the stabilizer of $(U, R, s, t, c)$ and let $G'$ be the stabilizer of $(U', R', s', t', c')$ . Then $G'$ is the base change of $G$ by $g$ , i.e., there is a canonical identification $G' = U' \times _{g, U} G$ .

Proof. Omitted. $\square$

Comments (0)

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).

Comments (0)

Post a comment