Ebook: Classgroups and Hermitian Modules
Author: A. Fröhlich (auth.)
- Tags: K-Theory, Algebraic Topology, Number Theory, Linear and Multilinear Algebras Matrix Theory, Algebraic Geometry, Group Theory and Generalizations
- Series: Progress in Mathematics 48
- Year: 1984
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
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.
Content:
Front Matter....Pages I-XVII
Preliminaries....Pages 1-19
Involution Algebras and the Hermitian Classgroup....Pages 20-77
Indecomposable Involution Algebras....Pages 78-116
Change of Order....Pages 117-145
Groups....Pages 146-197
Applications in Arithmetic....Pages 198-220
Back Matter....Pages 221-226
Content:
Front Matter....Pages I-XVII
Preliminaries....Pages 1-19
Involution Algebras and the Hermitian Classgroup....Pages 20-77
Indecomposable Involution Algebras....Pages 78-116
Change of Order....Pages 117-145
Groups....Pages 146-197
Applications in Arithmetic....Pages 198-220
Back Matter....Pages 221-226
....