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Preface

Preface to Complex

Multiplication of Abelian Varieties and Its Applications to Number Theory (1961)

Notation and Terminology

Preliminaries on Abelian Varieties / Ch I：

Abelian Varieties with Complex Multiplication / Ch II：

Reduction of Constant Fields / Ch III：

Construction of Class Fields / Ch IV：

The Zeta Function of an Abelian Variety with Complex Multiplication / Ch V：

Families of Abelian Varieties and Modular Functions / Ch VI：

Theta Functions and Periods on Abelian Varieties / Ch VII：

Bibliography

Supplementary

References

Index

Preface

Preface to Complex

Multiplication of Abelian Varieties and Its Applications to Number Theory (1961)

目次情報: 続きを見る

Introduction

Supersingular abelian varieties

Some prerequisites about group schemes

Flag type quotients

Main results on Sg,1 (the principally polarized case)

Prerequisites about Dieudonne modules

PFTQs of Dieudonnè modules over W

Moduli of rigid PFTQs of Dieudonnè modules

Some class numbers

Examples on Sg,1

Main results on Sg,d (the non-principally polarized case)

Proofs of the propositions on FTQs

Examples on Sg,d (d>1)

A scheme-theoretic definition of supersingularity

Appendix: Some historical remarks

References

Index

Introduction

Supersingular abelian varieties

Some prerequisites about group schemes