Arithmetic Duality Theorems

Name: Arithmetic Duality Theorems
Price: 44.55 USD
Availability: InStock
ISBN: 9780124980402

ISBN-10: 0124980406

ISBN-13: 9780124980402

Edition: 1986

Authors: James S. Milne

List price: $113.00

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Description:

Here, published for the first time, are the complete proofs of the fundamental arithmetic duality theorems that have come to play an increasingly important role in number theory and arithmetic geometry. The text covers these theorems in Galois cohomology, ,tale cohomology, and flat cohomology and addresses applications in the above areas. The writing is expository and the book will serve as an invaluable reference text as well as an excellent introduction to the subject.

Book details

List price: $113.00
Copyright year: 1986
Publisher: Elsevier Science & Technology Books
Publication date: 12/28/1986
Binding: Hardcover
Pages: 432
Size: 6.00" wide x 9.00" long x 1.22" tall
Weight: 1.848
Language: English



Preface


Notations and Conventions


Galois Cohomology


Preliminaries


Duality relative to a class formation


Local fields


Abelian varieties over local fields


Global fields


Global Euler-Poincare characteristics


Abelian varieties over global fields


An application to the conjecture of Birch and Swinnerton-Dyer


Abelian class field theory, in the sense of Langlands


Other applications


Class field theory for function fields


Etale Cohomology


Preliminaries


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


Preliminaries


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


Global results: curves over perfect fields


Embedding finite group schemes


Extending finite group schemes


Biextensions and Neron models


Bibliography


Index