Specialization of Quadratic and Symmetric Bilinear Forms

  • Manfred Knebusch

Part of the Algebra and Applications book series (AA, volume 11)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Manfred Knebusch, Thomas Unger
    Pages 1-53
  3. Manfred Knebusch, Thomas Unger
    Pages 55-90
  4. Manfred Knebusch, Thomas Unger
    Pages 91-164
  5. Manfred Knebusch, Thomas Unger
    Pages 165-183
  6. Back Matter
    Pages 185-192

About this book

Introduction

The specialization theory of quadratic and symmetric bilinear forms over fields and the subsequent generic splitting theory of quadratic forms were invented by the author in the mid-1970's. They came to fruition in the ensuing decades and have become an integral part of the geometric methods in quadratic form theory. This book comprehensively covers the specialization and generic splitting theories. These theories, originally developed mainly for fields of characteristic different from 2, are explored here without this restriction. In this book, a quadratic form φ over a field of characteristic 2 is allowed to have a big quasilinear part QL(φ) (defined as the restriction of φ to the radical of the bilinear form associated to φ), while in most of the literature QL(φ) is assumed to have dimension at most 1. Of course, in nature, quadratic forms with a big quasilinear part abound. In addition to chapters on specialization theory, generic splitting theory and their applications, the book's final chapter contains research never before published on specialization with respect to quadratic places and will provide the reader with a glimpse towards the future.

Keywords

DEX Generic splitting theory Quadratic forms Specialization theory Symmetric bilinear forms addition character form integral quadratic form quadratic places

Authors and affiliations

  • Manfred Knebusch
    • 1
  1. 1.Fak. Naturwissenschaft I, FB MathematikUniversität RegensburgRegensburgGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-84882-242-9
  • Copyright Information Springer-Verlag London Limited 2010
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-84882-241-2
  • Online ISBN 978-1-84882-242-9
  • Series Print ISSN 1572-5553
  • About this book