The Brauer group of $BG$ and gerbe structures of moduli spaces
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866909985496104960 |
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| author | Lopez, Rose |
| author_facet | Lopez, Rose |
| contents | We study the $μ_N$-gerbe of curves of genus $g$ with an order $N$ automorphism, and explore what corresponding $H^2$-cohomology classes the components of this stack can have. In particular, we look at curves whose quotients by the order $N$ automorphism are genus 0, and completely determine the Brauer classes of these gerbes. The key technical input is the calculation of the Brauer group of $BG$, for $G$ a smooth connected semisimple linear algebraic group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_05370 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Brauer group of $BG$ and gerbe structures of moduli spaces Lopez, Rose Algebraic Geometry 14D23, 14F22, 14H10 We study the $μ_N$-gerbe of curves of genus $g$ with an order $N$ automorphism, and explore what corresponding $H^2$-cohomology classes the components of this stack can have. In particular, we look at curves whose quotients by the order $N$ automorphism are genus 0, and completely determine the Brauer classes of these gerbes. The key technical input is the calculation of the Brauer group of $BG$, for $G$ a smooth connected semisimple linear algebraic group. |
| title | The Brauer group of $BG$ and gerbe structures of moduli spaces |
| topic | Algebraic Geometry 14D23, 14F22, 14H10 |
| url | https://arxiv.org/abs/2601.05370 |