Arithmetic duality theorems

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Arithmetic duality theorems / J.S. Milne

資料種別:: 図書
出版情報:: Boston ; Tokyo : Academic Press, c1986
形態:: x, 419 p. ; 24 cm
シリーズ名:: Perspectives in mathematics ; v. 1 <BA00333903>
著者名:: Milne, J. S., 1942- <DA00698647>
ISBN:: 9780124980402 [0124980406]
書誌ID:: BA00333856

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注記:

Bibliography: p. [410]-419
Includes index

主題:

Duality theory (Mathematics); Fields, Algebraic; Homology theory

言語:

英語

目次情報:

Preface

Notations and Conventions

Galois Cohomology / Chapter I：

Preliminaries / 0：

Duality relative to a class formation / 1：

Local fields / 2：

Abelian varieties over local fields / 3：

Global fields / 4：

Global Euler-Poincare characteristics / 5：

Abelian varieties over global fields / 6：

An application to the conjecture of Birch and Swinnerton-Dyer / 7：

Abelian class field theory, in the sense of Langlands / 8：

Other applications / 9：

Class field theory for function fields / Appendix A：

Etale Cohomology / Chapter II：

Local results

Global results: preliminary calculations

Global results: the main theorem

Global results: complements

Global results: abelian schemes

Global results: singular schemes

Global results: higher dimensions

Flat Cohomology / Chapter III：

Local results: mixed characteristic, finite group schemes

Local results: mixed characteristic, abelian varieties

Global results: number field case

Local results: mixed characteristic, perfect residue field

Two exact sequences

Local fields of characteristic p

Local results: equicharacteristic

Global results: curves over finite fields, finite sheaves

Global results: curves over finite fields, Neron models

Local results: equicharacteristic, perfect residue field / 10：

Global results: curves over perfect fields / 11：

Embedding finite group schemes

Extending finite group schemes / Appendix B：

Biextensions and Neron models / Appendix C：

Bibliography

Index

Preface

Notations and Conventions

Galois Cohomology / Chapter I：

Preliminaries / 0：

Duality relative to a class formation / 1：

Local fields / 2：

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