
Abelian Varieties with Complex Multiplication and Modular Functions
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This subject is closely connected with the zeta function of an abelian variety, which is also covered as a main theme in the book. The third topic explored by Shimura is the various algebraic relations among the periods of abelian integrals. The investigation of such algebraicity is relatively new, but has attracted the interest of increasingly many researchers. Many of the topics discussed in this book have not been covered before. In particular, this is the first book in which the topics of various algebraic relations among the periods of abelian integrals, as well as the special values of theta and Siegel modular functions, are treated extensively.
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Content
Preface to Complex Multiplication of Abelian Varieties and Its Applications to Number Theory (1961)
Notation and Terminology
Ch. I. Preliminaries on Abelian Varieties
Ch. II. Abelian Varieties with Complex Multiplication
Ch. III. Reduction of Constant Fields
Ch. IV. Construction of Class Fields
Ch. V. The Zeta Function of an Abelian Variety with Complex Multiplication
Ch. VI. Families of Abelian Varieties and Modular Functions
Ch. VII. Theta Functions and Periods on Abelian Varieties
Bibliography
Supplementary References
Index
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