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Multiplicative Galois Module Structure
 
A. Weiss :  University of Alberta, Edmonton, AB, Canada
A co-publication of the AMS and Fields Institute
Multiplicative Galois Module Structure
Multiplicative Galois Module Structure
Hardcover ISBN:  978-0-8218-0265-6
Product Code:  FIM/5
List Price: $56.00
MAA Member Price: $50.40
AMS Member Price: $44.80
eBook ISBN:  978-1-4704-3132-7
Product Code:  FIM/5.E
List Price: $53.00
MAA Member Price: $47.70
AMS Member Price: $42.40
Hardcover ISBN:  978-0-8218-0265-6
eBook: ISBN:  978-1-4704-3132-7
Product Code:  FIM/5.B
List Price: $109.00$82.50
MAA Member Price: $98.10$74.25
AMS Member Price: $87.20$66.00
Add to cart
Multiplicative Galois Module Structure
Click above image for expanded view
Multiplicative Galois Module Structure
Multiplicative Galois Module Structure
A. Weiss :  University of Alberta, Edmonton, AB, Canada
A co-publication of the AMS and Fields Institute
Hardcover ISBN:  978-0-8218-0265-6
Product Code:  FIM/5
List Price: $56.00
MAA Member Price: $50.40
AMS Member Price: $44.80
eBook ISBN:  978-1-4704-3132-7
Product Code:  FIM/5.E
List Price: $53.00
MAA Member Price: $47.70
AMS Member Price: $42.40
Hardcover ISBN:  978-0-8218-0265-6
eBook ISBN:  978-1-4704-3132-7
Product Code:  FIM/5.B
List Price: $109.00$82.50
MAA Member Price: $98.10$74.25
AMS Member Price: $87.20$66.00
Add to cart
  • Book Details
     
     
    Fields Institute Monographs
    Volume: 5; 1996; 95 pp
    MSC: 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.
    Readership

    Graduate 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 non-experts 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Fields Institute Monographs
Volume: 5; 1996; 95 pp
MSC: 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.
Readership

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 non-experts 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
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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