Friday, December 13, 2019 | 10:10am to 11:40am
About this Event
182 MEMORIAL DR, Cambridge, MA 02139
http://math.mit.edu/nt/index_stageSpeaker: Hood Chatham
Title: Lubin-Tate theory
Abstract:
If is a local field, local class field theory describes the behavior of the maximal abelian extension of
. It says that it is the composite of the maximal unramified abelian extension of
and a maximal totally ramified extension. The composite of any two unramified extensions is still unramified, so the maximal unramified extension is uniquely determined. The same is not true for totally ramified extensions, and in fact there is a maximal totally ramified extension
for each choice of uniformizer
of
.
Given a uniformizer of a local field
, Lubin and Tate constructed a formal
-module
. Using this formal group, they give an explicit construction of
by adjoining "
power torsion in
" to
. This allows an alternate construction of the Artin reciprocity map to the construction using Tate cohomology and an alternate proof of the theorems of local class field theory.
The talk will be accompanied by breakfast.