Scholarlink

We study a large family of generalized class groups of imaginary quadratic orders O and prove that they act freely and (essentially) transitively on the set of primitively O-oriented elliptic curves over a field k (assuming this set is non-empty) equipped with appropriate level structure. This extends, in several ways, a recent observation due to Galbraith, Perrin and Voloch for the ray class group. We show that this leads to a reinterpretation of the action of the class group of a suborder \(O' \subseteq O\) on the set of \(O'\) -oriented elliptic curves, discuss several other examples, and briefly comment on the hardness of the corresponding vectorization problems.

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Generalized Class Group Actions on Oriented Elliptic Curves with Level Structure

  • 会议论文

  • 发表日期：

    2025年

查看全文
  • Sarah Arpin,
  • Wouter Castryck,
  • Jonathan Komada Eriksen,
  • Gioella Lorenzon,
  • Frederik Vercauteren

摘要

We study a large family of generalized class groups of imaginary quadratic orders O and prove that they act freely and (essentially) transitively on the set of primitively O-oriented elliptic curves over a field k (assuming this set is non-empty) equipped with appropriate level structure. This extends, in several ways, a recent observation due to Galbraith, Perrin and Voloch for the ray class group. We show that this leads to a reinterpretation of the action of the class group of a suborder \(O' \subseteq O\) on the set of \(O'\) -oriented elliptic curves, discuss several other examples, and briefly comment on the hardness of the corresponding vectorization problems.