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Hardcover ISBN:  9780821802656 
Product Code:  FIM/5 
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Product Code:  FIM/5.E 
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AMS Member Price:  $42.40 
Hardcover ISBN:  9780821802656 
eBook ISBN:  9781470431327 
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Book DetailsFields Institute MonographsVolume: 5; 1996; 95 ppMSC: Primary 11; Secondary 16; 19; 20
This book is the result of a short course on the Galois structure of \(S\)units that was given at The Fields Institute in the fall of 1993. Offering a new angle on an old problem, the main theme is that this structure should be determined by class field theory, in its cohomological form, and by the behavior of Artin \(L\)functions at \(s=0\). A proof of this—or even a precise formulation—is still far away, but the available evidence all points in this direction. The work brings together the current evidence that the Galois structure of \(S\)units can be described.
Titles in this series are copublished with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
ReadershipGraduate students and research mathematicians, specifically algebraic number theorists.

Table of Contents

Chapters

Chapter 1. Overview

Chapter 2. From class field theory

Chapter 3. Extension classes

Chapter 4. Locally free class groups

Chapter 5. Tate sequences

Chapter 6. Recognizing $G$modules

Chapter 7. Local analogue

Chapter 8. $\Omega _m$ and the $G$module structure of $E$

Chapter 9. Artin $L$functions at $s = 0$

Chapter 10. $q$indices

Chapter 11. Parallel properties of $A_\varphi $ and $q_\varphi $

Chapter 12. $Q$valued characters

Chapter 13. Representing the Chinburg class

Chapter 14. Small $S$

Chapter 15. A cyclotomic example

Chapter 16. Notes


Reviews

No comparable work exists in the literature ... we should be thankful to have this book, which is at the same time an introduction, and a report on the state of the art, written by one of the leading experts ... Even nonexperts with some background in algebra should be able to profit from browsing in this book, which will be a standard reference for a long time to come.
Bulletin of the AMS


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This book is the result of a short course on the Galois structure of \(S\)units that was given at The Fields Institute in the fall of 1993. Offering a new angle on an old problem, the main theme is that this structure should be determined by class field theory, in its cohomological form, and by the behavior of Artin \(L\)functions at \(s=0\). A proof of this—or even a precise formulation—is still far away, but the available evidence all points in this direction. The work brings together the current evidence that the Galois structure of \(S\)units can be described.
Titles in this series are copublished with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
Graduate students and research mathematicians, specifically algebraic number theorists.

Chapters

Chapter 1. Overview

Chapter 2. From class field theory

Chapter 3. Extension classes

Chapter 4. Locally free class groups

Chapter 5. Tate sequences

Chapter 6. Recognizing $G$modules

Chapter 7. Local analogue

Chapter 8. $\Omega _m$ and the $G$module structure of $E$

Chapter 9. Artin $L$functions at $s = 0$

Chapter 10. $q$indices

Chapter 11. Parallel properties of $A_\varphi $ and $q_\varphi $

Chapter 12. $Q$valued characters

Chapter 13. Representing the Chinburg class

Chapter 14. Small $S$

Chapter 15. A cyclotomic example

Chapter 16. Notes

No comparable work exists in the literature ... we should be thankful to have this book, which is at the same time an introduction, and a report on the state of the art, written by one of the leading experts ... Even nonexperts with some background in algebra should be able to profit from browsing in this book, which will be a standard reference for a long time to come.
Bulletin of the AMS