Math 845 - Spring 2005

Nigel Boston

Contact Information

303 Van Vleck Hall.

Telephone: 263-4753.



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


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.


Homework Assignments

Some Lists of Unsolved Problems

General Information (e.g. Conferences)

Online Notes

Books on Class Field Theory

History of Class Field Theory