Fields Institute Monographs
Volume: 5;
1996;
95 pp;
Hardcover
MSC: Primary 11;
Secondary 16; 19; 20
Print ISBN: 978-0-8218-0265-6
Product Code: FIM/5
List Price: $50.00
AMS Member Price: $40.00
MAA Member Price: $45.00
Electronic ISBN: 978-1-4704-3132-7
Product Code: FIM/5.E
List Price: $50.00
AMS Member Price: $40.00
MAA Member Price: $45.00
Multiplicative Galois Module Structure
Share this pageA. Weiss
A co-publication of the AMS and Fields Institute
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 co-published with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
Readership
Graduate students and research mathematicians, specifically algebraic number theorists.
Reviews & Endorsements
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
Table of Contents
Table of Contents
Multiplicative Galois Module Structure
- Cover Cover11
- Title page iii4
- Contents v6
- List of results vi7
- Preface vii8
- Overview 110
- From class field theory 716
- Extension classes 1120
- Locally free class groups 1726
- Tate sequences 2332
- Recognizing ๐บ-modules 3342
- Local analogue 4150
- ๐๐๐๐๐_{๐} and the ๐บ-module structure of ๐ธ 4756
- Artin ๐ฟ-functions at ๐ =0 4958
- ๐-indices 5362
- Parallel properties of ๐ด_{๐} and ๐_{๐} 5766
- ๐-valued characters 6978
- Representing the Chinburg class 7180
- Small ๐ 7988
- A cyclotomic example 8594
- Notes 8998
- Bibliography 93102
- Subject index 95104
- Copying/Reprinting page 96105
- Back Cover Back Cover1106