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arXiv · 2603.21702

Neutral representations of finite diagonalizable group schemes and fields of moduli

Giulio Bresciani·Angelo Vistoli·Tianzhi Yang
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Abstract

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.

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Giulio Bresciani, Angelo Vistoli, Tianzhi Yang. 2026-03-23. Neutral representations of finite diagonalizable group schemes and fields of moduli. https://arxiv.org/abs/2603.21702

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