---
date: 2022-04-05 23:42
modification date: Friday 8th April 2022 13:35:56
title: "Lubin-Tate theory"
aliases: ["Lubin-Tate"]
---

Last modified date: <%+ tp.file.last_modified_date() %>

---
- Tags: 
	- #todo/untagged
- Refs:
	- Lubin-Tate *Formal Groups* #resources/books 
	 - See *J. Lubin and J. Tate, Formal complex multiplication in local fields* #resources/books 
	 - For their deformation spaces, see *Formal moduli for one parameter formal Lie groups* #resources/books 
- Links:
	- [Formal group](Unsorted/Formal%20group.md)

---

# Lubin-Tate theory

An alternative approach to [CFT](Unsorted/class%20field%20theory.md) leading to a nonabelian variant:
![](attachments/Pasted%20image%2020220508194409.png)

# Motivation

![](attachments/Pasted%20image%2020220408133558.png)

# Spectra
![](attachments/Pasted%20image%2020220209191957.png)
![](attachments/Pasted%20image%2020220209192054.png)

# Relation to CFT

See [CFT](Unsorted/class%20field%20theory.md) and [maximal abelian extension](maximal%20abelian%20extension)
![](attachments/Pasted%20image%2020220508201139.png)
![](attachments/Pasted%20image%2020220508201256.png)
![](attachments/Pasted%20image%2020220508201322.png)

See [Artin map](Unsorted/Artin%20symbol.md).

![](attachments/Pasted%20image%2020220508201350.png)

# Examples

![](attachments/Pasted%20image%2020220508201439.png)