# Specialization of Quadratic and Symmetric Bilinear Forms

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

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

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.

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

- 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
- Buy this book on publisher's site

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