Complex Multiplication - 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

pdf file for the current version (0.00)
### Contents

### History

Version 0; April 7, 2006; 113 pages.

These are preliminary notes for a modern account of the theory of complex multiplication. The article
*The fundamental theorem of complex multiplication (2007)* is a much improved version of part of
this work, so probably the two should be read together. (These notes don't, in fact, correspond to any course I've taught, but it is
convenient to include them here.)

- Analytic theory
- Arithmetic theory
- CM-motives
- Applications