---
created: 2022-04-05T23:42
updated: 2024-03-04T19:07
aliases:
  - ray class
  - ray class group
---
Tags: 
#todo #todo/stub 
Refs:
[Kronecker-Weber theorem](Unsorted/Kronecker-Weber%20theorem.md)
[Artin reciprocity](Unsorted/Artin%20symbol.md)
[Hilbert class field](Hilbert%20class%20field)
[idele](Adeles.md)

![](2024-03-04-2.png)

# Motivation

![](attachments/Pasted%20image%2020220126164350.png)

# ray class field

![](attachments/Pasted%20image%2020220126164227.png)
![](attachments/Pasted%20image%2020220126162423.png)
![](attachments/Pasted%20image%2020220126162914.png)
![](attachments/Pasted%20image%2020220126163000.png)
![](attachments/Pasted%20image%2020220126163156.png)

![](attachments/Pasted%20image%2020220126163222.png)

![](attachments/Pasted%20image%2020220126163240.png)
![](attachments/Pasted%20image%2020220126163323.png)

# Examples

![](attachments/Pasted%20image%2020220126163413.png)

## Ray class group

![](attachments/2023-01-12-2.png)
![](attachments/2023-01-12-3.png)

![](attachments/2023-01-12-4.png)