Complex Multiplication - J.S. Milne   Top
Course Notes
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)

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.)


  1. Analytic theory
  2. Arithmetic theory
  3. CM-motives
  4. Applications


Version 0; April 7, 2006; 113 pages.