Definition 101.28.1 (06QC)—The Stacks project

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Table of contents
Part 7: Algebraic Stacks
Chapter 101: Morphisms of Algebraic Stacks
Section 101.28: Gerbes
Definition 101.28.1 (cite)

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Definition 101.28.1. Let $f : \mathcal{X} \to \mathcal{Y}$ be a morphism of algebraic stacks. We say $\mathcal{X}$ is a gerbe over $\mathcal{Y}$ if $\mathcal{X}$ is a gerbe over $\mathcal{Y}$ as stacks in groupoids over $(\mathit{Sch}/S)_{fppf}$ , see Stacks, Definition 8.11.4. We say an algebraic stack $\mathcal{X}$ is a gerbe if there exists a morphism $\mathcal{X} \to X$ where $X$ is an algebraic space which turns $\mathcal{X}$ into a gerbe over $X$ .

Comments (2)

Comment #3223 by typo on March 14, 2018 at 10:12

In the text between Definition 92.27.1 and Lemma 92.27.2 there is a reference to Lemma 92.27.7. The reference should be 92.27.8.

Comment #3325 by Johan on May 19, 2018 at 12:03

Thanks, fixed here.

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