Brauer groups of tame stacky curves and their μᵣ-gerbes

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This is a Quantitative Study study.

Martin Bishop

doi:10.48550/arxiv.2507.08780

July 11, 2025Open Access

Brauer groups of tame stacky curves and their μᵣ-gerbes

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Key Points

The Brauer group of a μ_r-gerbe fits into an exact sequence, revealing its structural properties.
Conditions for the Brauer group to be short exact and for it to split are precisely characterized.
A formula for the Brauer group is provided specifically for cases where the base curve is smooth.
This work extends the understanding of brauer groups within the context of possibly singular stacky curves.

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Implication

Characterization of the Brauer group of μ_r-gerbes in stacky curves, highlighting when it is short exact.

Abstract

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

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Cite This Study

Martin Bishop (2025) studied this question.

synapsesocial.com/papers/68f163c79903599108abcd9d https://doi.org/10.48550/arxiv.2507.08780

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Brauer groups of tame stacky curves and their μᵣ-gerbes

Key Points

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Implication

Abstract

Discussion

Cite This Study

Brauer groups of tame stacky curves and their μᵣ-gerbes

Key Points

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Implication

Abstract

Discussion

Cite This Study

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