Brauer groups of tame stacky curves and their μ_r-gerbes

2025/07/11 by Martin Bishop, Bishop, Martin
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2507.08780

openalex publication_date 2025/07/11 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

We fit the Brauer group of a μ_r-gerbe over a (possibly arbitrarily singular) stacky curve into an exact sequence and give characterizations for when it is short exact and conditions for when it splits. We also give a precise formula for the Brauer group of a μ_r-gerbe in the case that the base curve is smooth.

Citations

• On Brauer groups of tame stacks
• Picard Groups of Stacky Curves
• Tame stacks in positive characteristic

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• Picard Groups of Stacky Curves
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