ENGLISH

Specialization of Quadratic and Symmetric Bilinear Forms

By Manfred Knebusch (auth.)

Book information

Publisher
Springer-Verlag London
Year
2010
ISBN
1848822413, 9781848822412
DOI
10.1007/978-1-84882-242-9
Language
english
Format
PDF
Filesize
2 MB (2254009 bytes)
Series
Algebra and Applications 11
Edition
1
Pages
192\208
Time added
2011-06-04 13:46:07
Algebra

Description

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.

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