Fields Institute Monographs 1996; 95 pp; hardcover Volume: 5 ISBN10: 0821802658 ISBN13: 9780821802656 List Price: US$47 Member Price: US$37.60 Order Code: FIM/5
 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 thisor even a precise formulationis 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). Readership Graduate students and research mathematicians, specifically algebraic number theorists. 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 Table of Contents  Overview
 From class field theory
 Extension classes
 Locally free class groups
 Tate sequences
 Recognizing \(G\)modules
 Local analogue
 \(\Omega _m\) and the \(G\)module structure of \(E\)
 Artin \(L\)functions at \(s=0\)
 \(q\)indices
 Parallel properties of\(A_\varphi\) and \(A_\varphi\)
 \(\mathbb Q\)valued characters
 Representing the Chinburg class
 Small \(S\)
 A cyclotomic example
 Notes
 Bibliography
 Subject index
