Class Field Theory - J.S. Milne Top

Group Theory

Fields and Galois Theory

Algebraic Geometry

Algebraic Number Theory

Modular Functions and Modular Forms

Elliptic Curves -- see books.

Abelian Varieties

Lectures on Etale Cohomology

Class Field Theory

Complex Multiplication

Basic Theory of Affine Group Schemes

Lie Algebras, Algebraic Groups, and Lie Groups

Reductive Groups

Errata

pdf file for the current version (4.02)
### Contents

### Prerequisites

The algebra usually covered in first-year graduate courses and a course in
algebraic number theory (for example, my online notes).
### History

v2.01; first version on the web.

v3.10; May 6, 1997; substantially revised and expanded from v2.01; index; 222 pages.

v4.00; March 2, 2008; corrected, revised, and expanded; 287 pages.

v4.01; May 30, 2011; corrected; 287 pages.

v4.02; March 23, 2013; corrected; 289 pages.

This is a course on Class Field Theory, roughly along the lines of Artin and Tate and of the articles of Serre and Tate in Cassels-Fröhlich, except that the notes are more detailed and cover more.

- Local Class Field Theory: Lubin-Tate Extensions
- Cohomology of Groups.
- Local Class Field Theory Continued.
- Brauer Groups
- Global Class Field Theory: Statements
- L-series and the Density of Primes
- Global Class Field Theory: Proofs
- Complements (Power reciprocity laws; quadratic forms; etc.)

v3.10; May 6, 1997; substantially revised and expanded from v2.01; index; 222 pages.

v4.00; March 2, 2008; corrected, revised, and expanded; 287 pages.

v4.01; May 30, 2011; corrected; 287 pages.

v4.02; March 23, 2013; corrected; 289 pages.