1998/06/15 by J. S. Milne, James S. Milne, Milne, James S.
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Meromorphic and Entire Functions #math.NT
paper · pdf · doi:10.48550/arxiv.math/9806172
arxiv created 1998/06/15 · arxiv updated 2009/12/01
This is the text of an article that I wrote and disseminated in September 1981, except that I've updated the references, corrected a few misprints, and added a table of contents, some footnotes, and an addendum. The original article gave a simplified exposition of Deligne's extension of the Main Theorem of Complex Multiplication to all automorphisms of the complex numbers. The addendum discusses some additional topics in the theory of complex multiplication -- the origins of the theory, Hilbert's Twelfth Problem, why algebraic Hecke characters are motivic, and the periods of abelian varieties of CM-type. (43 pages)