Neutral representations of finite diagonalizable group schemes and fields of moduli
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918403357278208 |
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| author | Bresciani, Giulio Vistoli, Angelo Yang, Tianzhi |
| author_facet | Bresciani, Giulio Vistoli, Angelo Yang, Tianzhi |
| contents | We introduce the notion of a neutral representation of a finite group, or finite group scheme, $G$; a representation $V$ with the property that if a gerbe $\mathcal{G}$ over a field $k$ that is a form of the classifying stack $\mathcal{B} G$ admits a vector bundle that is a form of $V$, then it is neutral, that is, $\mathcal{G}(k)$ is not empty. We give some criteria for a representation of a finite diagonalizable group scheme to be neutral.
We apply this notion to give wide classes of examples of smooth curves, or varieties with a marked point, with cyclic automorphism groups, which are defined over their field of moduli, greatly generalizing some previous results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21702 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Neutral representations of finite diagonalizable group schemes and fields of moduli Bresciani, Giulio Vistoli, Angelo Yang, Tianzhi Algebraic Geometry Number Theory We introduce the notion of a neutral representation of a finite group, or finite group scheme, $G$; a representation $V$ with the property that if a gerbe $\mathcal{G}$ over a field $k$ that is a form of the classifying stack $\mathcal{B} G$ admits a vector bundle that is a form of $V$, then it is neutral, that is, $\mathcal{G}(k)$ is not empty. We give some criteria for a representation of a finite diagonalizable group scheme to be neutral. We apply this notion to give wide classes of examples of smooth curves, or varieties with a marked point, with cyclic automorphism groups, which are defined over their field of moduli, greatly generalizing some previous results. |
| title | Neutral representations of finite diagonalizable group schemes and fields of moduli |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2603.21702 |