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Field name	Details
Dewey Class	512.66
Title	Classgroups and Hermitian Modules ([EBook]) / by A. Fröhlich
Author	Fröhlich, Albrecht
Other name(s)	SpringerLink (Online service)
Publication	Boston, MA : Birkhäuser , 1984
Physical Details	XVIII, 226 pages : online resource.
Series	Progress in mathematics 0743-1643 ; ; 48
ISBN	9781468467406
Summary Note	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.:
Contents note	I Preliminaries -- §1 Locally free modules and locally freely presented torsion modules -- §2 Determinants and the Hom language for classgroups -- §3 Supplement at infinity -- II Involution algebras and the Hermitian classgroup -- §1 Involution algebras and duality -- §2 Hermitian modules -- §3 Pfaffians of matrices -- §4 Pfaffians of algebras -- §5 Discriminants and the Hermitian classgroup -- §6 Some homomorphisms -- §7 Pulling back discriminants -- §8 Unimodular modules -- §8 Products -- III Indecomposable involution algebras -- §1 Dictionary -- §2 The map P -- §3 Discriminants once more -- §4 Norms of automorphisms -- §5 Unimodular classes once more -- IV Change of order -- §1 Going up -- §2 Going down -- V Groups -- §1 Characters -- §2 Character action. Ordinary theory -- §3 Character action. Hermitian theory -- §4 Special formulae -- §5 Special properties of the group ring involution -- §6 Some Frobenius modules -- §7 Some subgroups of the adelic Hermitian classgroup -- VI Applications in arithmetic -- §1 Local theory -- §2 The global discriminant -- Literature -- List of Theorems -- Some further notation.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4684-6740-6
Links to Related Works	Subject References: Algebra . Algebraic Geometry . Algebraic Topology . Group theory . K-Theory . Mathematics . Matrix theory . Number Theory . Authors: Fröhlich, Albrecht . Corporate Authors: SpringerLink (Online service) . Series: Progress in mathematics . Classification: 512.66 .

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Classgroups and Hermitian Modules

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