Infinite places

---
date: 2022-01-15 21:49
modification date: Monday 24th January 2022 10:17:42
title: conductor
aliases: [conductor]

---

Tags: 
#todo #todo/stub 
Refs:
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# Conductor of a ring

Idea: for $A\leq_{\Ring} B$ with $B$ integral over $A$, the **conductor** $\mfc(B\slice A)$ is the largest ideal $I \in \Id(A) \intersect \Id(B)$. Equivalently, $\mfc(B\slice A) = \Ann_{\mods{A}}(B/A)$.

![](attachments/Pasted%20image%2020220124101714.png)

# Conductor of an [order](order.md)
![](attachments/Pasted%20image%2020211005011042.png)

# Conductor of an extension
![](attachments/Pasted%20image%2020220126164438.png)

# Conductor of an abelian extension

![](attachments/Pasted%20image%2020220126165905.png)
# Conductor of an elliptic curve

#todo