论文标题
射线类组和射线类字段，用于数字字段的订单
Ray class groups and ray class fields for orders of number fields
论文作者
论文摘要
本文有助于数字字段的顺序理论。本文定义了一个与该顺序的任意射线类模量（包括阿基米德数据）相关联的“射线类组”的概念，该概念是使用订单的可逆分数理想构建的。它显示了与类组相对应的“射线类字段”的存在。在最大秩序的情况下，这些射线类组（分别，射线类字段）专门针对一个数字的经典射线类组（分别，域），并且在琐碎模量的情况下，它们专门针对阶段组（分别为，，分别为，，分别）。该论文给出了同时更改顺序和模量更改的精确序列。结果，我们将带有模量的顺序的射线类字段识别为具有较大模量的最大顺序的射线类字段的特定子场。我们还唯一地描述了订单的每个射线类字段。
This paper contributes to the theory of orders of number fields. This paper defines a notion of "ray class group" associated to an arbitrary order in a number field together with an arbitrary ray class modulus for that order (including Archimedean data), constructed using invertible fractional ideals of the order. It shows existence of "ray class fields" corresponding to the class groups. These ray class groups (resp., ray class fields) specialize to classical ray class groups (resp., fields) of a number field in the case of the maximal order, and they specialize to ring class groups (resp., fields) of orders in the case of trivial modulus. The paper gives exact sequences for simultaneous change of order and change of modulus. As a consequence, we identify the ray class field of an order with a given modulus as a specific subfield of a ray class field of the maximal order with a larger modulus. We also uniquely describe each ray class field of an order in terms of the splitting behavior of primes.
