Brauer groups of tame stacky curves and their $\mu_r$-gerbes

Martin Bishop

Brauer groups of tame stacky curves and their $\mu_r$-gerbes

Algebraic Geometry 2025-07-25 v2

Authors: Martin Bishop

Abstract

We fit the Brauer group of a $\mu_r$ -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 $\mu_r$ -gerbe in the case that the base curve is smooth.

Keywords

Brauer group stacky curves $\mu_r$-gerbe exact sequence smooth curve

Cite

@article{arxiv.2507.08780,
  title  = {Brauer groups of tame stacky curves and their $\mu_r$-gerbes},
  author = {Martin Bishop},
  journal= {arXiv preprint arXiv:2507.08780},
  year   = {2025}
}

Comments

24 pages. Rewrote intro, reorganized background, removed extraneous result, mild improvements throughout

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