Neutral representations of finite diagonalizable group schemes and fields of moduli
Algebraic Geometry
2026-03-24 v1 Number Theory
Abstract
We introduce the notion of a neutral representation of a finite group, or finite group scheme, ; a representation with the property that if a gerbe over a field that is a form of the classifying stack admits a vector bundle that is a form of , then it is neutral, that is, 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.
Keywords
Cite
@article{arxiv.2603.21702,
title = {Neutral representations of finite diagonalizable group schemes and fields of moduli},
author = {Giulio Bresciani and Angelo Vistoli and Tianzhi Yang},
journal= {arXiv preprint arXiv:2603.21702},
year = {2026}
}