The structure of regular genus-one curves over imperfect fields

2022/11/08 by Stefan Schröer, Schröer, Stefan
Computer Science · Mathematics · #14B05 #14D06 #14G17 #14H45 #14L30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2211.04073

openalex publication_date 2022/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Working over imperfect fields, we give a comprehensive classification of genus-one curves that are regular but not geometrically regular, extending the known case of geometrically reduced curves. The description is given intrinsically, in terms of twisted forms of standard models with respect to infinitesimal group scheme actions, and not via extrinsic equations. The main new idea is to analyze and exploit moduli for fields of representatives in Cohen's Structure Theorem. The results serve for the understanding of genus-one fibrations over higher-dimensional bases.

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• Moduli of Curves of Genus One with Twisted Fields
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• Invariants of models of genus one curves and modular forms
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