Lemma 101.28.5 (06QF)—The Stacks project

Processing math: 100%

Table of contents
Part 7: Algebraic Stacks
Chapter 101: Morphisms of Algebraic Stacks
Section 101.28: Gerbes
Lemma 101.28.5 (cite)

previous lemma
next lemma

numberstags

history
statistics
2 tags refer to this tag

$\xymatrix{ \mathcal{X}' \ar[r] \ar[d] & \mathcal{X} \ar[d] \\ \mathcal{Y}' \ar[r] & \mathcal{Y} }$

be a fibre product of algebraic stacks. If $\mathcal{Y}' \to \mathcal{Y}$ is surjective, flat, and locally of finite presentation and $\mathcal{X}'$ is a gerbe over $\mathcal{Y}'$ , then $\mathcal{X}$ is a gerbe over $\mathcal{Y}$ .

Proof. Follows immediately from Lemma 101.27.13 and Stacks, Lemma 8.11.7. $\square$

Comments (0)

There are also:

2 comment(s) on Section 101.28: Gerbes

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