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
Abelian Varieties
Lectures on Etale Cohomology
Class Field Theory
Complex Multiplication
Algebraic Groups; Lie Algebras; Lie Groups; Reductive Groups
Errata
pdf file for the current version (0.10)

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.)

Contents

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

History

v0.00, April 7, 2006; 113 pages.
v0.10, July 14, 2020. Updated TeX; minor fixes; 108 pages.