Classgroups and Hermitian Modules:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Boston, MA
Birkhäuser Boston
1984
|
| Series: | Progress in Mathematics
48 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | 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 |
| Physical Description: | 1 Online-Ressource (XVIII, 226p) |
| ISBN: | 9781468467406 9781468467420 |
| DOI: | 10.1007/978-1-4684-6740-6 |
Staff View
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| indexdate | 2024-07-10T01:21:08Z |
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| isbn | 9781468467406 9781468467420 |
| language | English |
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| spelling | Fröhlich, Albrecht 1916-2001 Verfasser (DE-588)124101852 aut Classgroups and Hermitian Modules by A. Fröhlich Boston, MA Birkhäuser Boston 1984 1 Online-Ressource (XVIII, 226p) txt rdacontent c rdamedia cr rdacarrier Progress in Mathematics 48 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 Mathematics Geometry, algebraic Group theory K-theory Matrix theory Number theory Algebraic topology K-Theory Algebraic Topology Number Theory Linear and Multilinear Algebras, Matrix Theory Algebraic Geometry Group Theory and Generalizations Mathematik Hermitesche Klassengruppe (DE-588)4159613-4 gnd rswk-swf Klasse Mathematik (DE-588)4312814-2 gnd rswk-swf Modul (DE-588)4129770-2 gnd rswk-swf Klassengruppe (DE-588)4164018-4 gnd rswk-swf Klasse Mathematik (DE-588)4312814-2 s Modul (DE-588)4129770-2 s 1\p DE-604 Hermitesche Klassengruppe (DE-588)4159613-4 s 2\p DE-604 Klassengruppe (DE-588)4164018-4 s 3\p DE-604 https://doi.org/10.1007/978-1-4684-6740-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Fröhlich, Albrecht 1916-2001 Classgroups and Hermitian Modules Mathematics Geometry, algebraic Group theory K-theory Matrix theory Number theory Algebraic topology K-Theory Algebraic Topology Number Theory Linear and Multilinear Algebras, Matrix Theory Algebraic Geometry Group Theory and Generalizations Mathematik Hermitesche Klassengruppe (DE-588)4159613-4 gnd Klasse Mathematik (DE-588)4312814-2 gnd Modul (DE-588)4129770-2 gnd Klassengruppe (DE-588)4164018-4 gnd |
| subject_GND | (DE-588)4159613-4 (DE-588)4312814-2 (DE-588)4129770-2 (DE-588)4164018-4 |
| title | Classgroups and Hermitian Modules |
| title_auth | Classgroups and Hermitian Modules |
| title_exact_search | Classgroups and Hermitian Modules |
| title_full | Classgroups and Hermitian Modules by A. Fröhlich |
| title_fullStr | Classgroups and Hermitian Modules by A. Fröhlich |
| title_full_unstemmed | Classgroups and Hermitian Modules by A. Fröhlich |
| title_short | Classgroups and Hermitian Modules |
| title_sort | classgroups and hermitian modules |
| topic | Mathematics Geometry, algebraic Group theory K-theory Matrix theory Number theory Algebraic topology K-Theory Algebraic Topology Number Theory Linear and Multilinear Algebras, Matrix Theory Algebraic Geometry Group Theory and Generalizations Mathematik Hermitesche Klassengruppe (DE-588)4159613-4 gnd Klasse Mathematik (DE-588)4312814-2 gnd Modul (DE-588)4129770-2 gnd Klassengruppe (DE-588)4164018-4 gnd |
| topic_facet | Mathematics Geometry, algebraic Group theory K-theory Matrix theory Number theory Algebraic topology K-Theory Algebraic Topology Number Theory Linear and Multilinear Algebras, Matrix Theory Algebraic Geometry Group Theory and Generalizations Mathematik Hermitesche Klassengruppe Klasse Mathematik Modul Klassengruppe |
| url | https://doi.org/10.1007/978-1-4684-6740-6 |
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