Math 249
Over two quarters, this course will focus on the class field
theory, including the construction of the Weil group and the
theories of Hecke and Artin Lfunctions. We will begin with
class field theory. The course should be quite different
from Rubin's course last year, however.
Announcements
Course materials
Other resources

Hochschild's review of Weil's 1951 paper on class field theory.

Peter Roquette's homepage contains many historical papers
on the origins of modern algebraic number theory. For example,
the paper The HasseBrauerNoether theorem in historical
perspective is directly relevant to our subject matter.

Milne's notes on class field theory.
 Gauss
first proved the quadratic reciprocity law, leading to further developments
of reciprocity laws by
Eisenstein and
Kummer.
Hilbert
in his 1897 Zahlbericht gave a profound analysis of Kummer's work
leading to the notion of a class field. The main theorems of Class Field
Theory were proved before 1920 by
Takagi. Artin
clarified the foundations by elucidating the special role of the
Frobenius
map, inventing the Artin Lfunctions, and giving lucid expositions of the
theory. Meanwhile in 1932
Hasse, Brauer
and Noether
determined the structure of division algebras over local and global fields,
allowing new foundations for class field theory. Ideles and Adeles were
introduced by
Chevalley
and
Weil,
allowing a more streamlined treatment of the global theory. Finally Weil
introduced the Weil group in 1951, and the role of Galois cohomology
was clarified by Hochschild, Artin and Tate.
Last modified: Mon Jan 3 17:13:14 2005