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arXiv · 2509.08529

On the unit group scheme of the group algebra of a certain non-commutative finite flat group scheme over an $\Bbb{F}_{p}$-algebra

Yuji Tsuno
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Abstract

Suwa investigated the unit group scheme of the group ring associated with a finite flat group scheme and provided a characterization of torsors possessing the normal base property for such schemes. In this paper, we examine the unit group scheme of the group ring for a specific non-commutative finite flat group scheme and characterize torsors with the normal base property in this context. Moreover, in connection with the Noether problem for Hopf algebras proposed by Kassel and Masuoka, we compute the quotient of the unit group scheme under the action of this non-commutative finite flat group scheme.

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Yuji Tsuno. 2025-09-10. On the unit group scheme of the group algebra of a certain non-commutative finite flat group scheme over an $\Bbb{F}_{p}$-algebra. https://arxiv.org/abs/2509.08529

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