# Math 845 - Spring 2005

# Nigel Boston

## Contact Information

303 Van Vleck Hall.
Telephone: 263-4753.

E-mail: *boston@math.wisc.edu*

Homepage

Office Hours: T 1-2:30 in 303 VV or W 10:30-12 in 3619 EH, or by appointment.

## Text

Milne's notes
## Course Overview

Class field theory is the description of extensions of a number field (or local field) K in terms of the arithmetic of K.
For extensions with abelian Galois group, the theory was the focal point of algebraic number theory from about 1850 to 1930. The nonabelian
case has many conjectures but few proofs. In this course abelian class field theory will be completely covered, requiring the introduction
of many of the tools in the armory of the modern number theorist, such as Galois cohomology, L-series, etc. Applications of historical
and modern importance will be presented en route together with several concrete examples. Check out Milne's notes to learn more.
## Sections

- Main Lecture: TR 2:30-3:45 B131 VV.

## Homework Assignments

- 1st Homework, pdf version
- 1st Homework, ps version
- 2nd Homework, pdf version
- 2nd Homework, ps version
- 3rd Homework, pdf version
- 3rd Homework, ps version
- 4th Homework, pdf version
- 4th Homework, ps version
- 5th Homework, pdf version
- 5th Homework, ps version

## Some Lists of Unsolved Problems

## General Information (e.g. Conferences)

## Online Notes

## Books on Class Field Theory

## History of Class Field Theory