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Progress in Mathematics

Classgroups and Hermitian Modules

Authors: Fröhlich, Albrecht

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About this book

These notes are an expanded and updated version of a course of lectures which I gave at King's College London during the summer term 1979. The main topic is the Hermitian classgroup of orders, and in particular of group rings. Most of this work is published here for the first time. The primary motivation came from the connection with the Galois module structure of rings of algebraic integers. The principal aim was to lay the theoretical basis for attacking what may be called the "converse problem" of Galois module structure theory: to express the symplectic local and global root numbers and conductors as algebraic invariants. A previous edition of these notes was circulated privately among a few collaborators. Based on this, and following a partial solution of the problem by the author, Ph. Cassou-Nogues and M. Taylor succeeded in obtaining a complete solution. In a different direction J. Ritter published a paper, answering certain character theoretic questions raised in the earlier version. I myself disapprove of "secret circulation", but the pressure of other work led to a delay in publication; I hope this volume will make amends. One advantage of the delay is that the relevant recent work can be included. In a sense this is a companion volume to my recent Springer-Ergebnisse-Bericht, where the Hermitian theory was not dealt with. Our approach is via "Hom-groups", analogous to that followed in recent work on locally free classgroups.

Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook $79.99
price for USA in USD
  • ISBN 978-1-4684-6740-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Classgroups and Hermitian Modules
Authors
Series Title
Progress in Mathematics
Series Volume
48
Copyright
1984
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston, Inc.
eBook ISBN
978-1-4684-6740-6
DOI
10.1007/978-1-4684-6740-6
Softcover ISBN
978-1-4684-6742-0
Series ISSN
0743-1643
Edition Number
1
Number of Pages
XVIII, 226
Topics

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