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

Lubin-Tate theory

An alternative approach to CFT leading to a nonabelian variant: attachments/Pasted%20image%2020220508194409.png

Motivation

attachments/Pasted%20image%2020220408133558.png

Spectra

attachments/Pasted%20image%2020220209191957.png

Relation to CFT

See CFT and maximal abelian extension attachments/Pasted%20image%2020220508201139.png

See Artin map.

attachments/Pasted%20image%2020220508201350.png

Examples

attachments/Pasted%20image%2020220508201439.png

Links to this page

class field theory

Lubin-Tate
Formal group

The universal deformations of the Honda formal group laws, \(\tilde H_{n, p}\) correspond to Morava E theory \(E_{n, p}\), which live over the Lubin-Tate rings \(\LT_{ H_{n, p} {}_{/ {{ \mathbf{F} }_p}} }= { {\mathbf{Z}}_{\widehat{p}} }{\left[\left[ u_1,\cdots, u_{n-1} \right]\right] }\).