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Specialization of quadratic and symmetric bilinear forms

Author: Manfred Knebusch
Publisher: London ; New York : Springer, ©2010.
Series: Algebras and applications, 11.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
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,  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Knebusch, Manfred.
Specialization of quadratic and symmetric bilinear forms.
London ; New York: Springer, ©2010
(DLC) 2010931863
(OCoLC)646114290
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Manfred Knebusch
ISBN: 9781848822429 1848822421
OCLC Number: 701718760
Description: 1 online resource (xiv, 192 pages) : illustrations.
Contents: Cover13; --
Preface --
Contents --
1 Fundamentals of Specialization Theory --
1.1 Introduction: on the Problem of Specialization of Quadratic and Bilinear Forms --
1.2 An Elementary Treatise on Symmetric Bilinear Forms --
1.3 Specialization of Symmetric Bilinear Forms --
1.4 Generic Splitting in Characteristic 2 --
1.5 An Elementary Treatise on Quadratic Modules --
1.6 Quadratic Modules over Valuation Rings --
1.7 Weak Specialization --
1.8 Good Reduction --
2 Generic Splitting Theory --
2.1 Generic Splitting of Regular Quadratic Forms --
2.2 Separable Splitting --
2.3 Fair Reduction and Weak Obedience --
2.4 Unified Theory of Generic Splitting --
2.5 Regular Generic Splitting Towers and Base Extension --
2.6 Generic Splitting Towers of a Specialized Form --
3 Some Applications --
3.1 Subforms which have Bad Reduction --
3.2 Some Forms of Height 1 --
3.3 The Subform Theorem --
3.4 Milnor's Exact Sequence --
3.5 A Norm Theorem --
3.6 Strongly Multiplicative Forms --
3.7 Divisibility by Pfister Forms --
3.8 Pfister Neighbours and Excellent Forms --
3.9 Regular Forms of Height 1 --
3.10 Some Open Problems in Characteristic 2 --
3.11 Leading Form and Degree Function --
3.12 The Companion Form of an Odd-dimensional Regular Form --
3.13 Definability of the Leading Form over the Base Field --
4 Specialization with Respect to Quadratic Places --
4.1 Quadratic Places; Specialization of Bilinear Forms --
4.2 Almost Good Reduction with Respect to Extensions of Quadratic Places --
4.3 Realization of Quadratic Places; Generic Splitting of Specialized Forms in Characteristic 2 --
4.4 Stably Conservative Reduction of Quadratic Forms --
4.5 Generic Splitting of Stably Conservative Specialized Quadratic Forms --
References --
Index.
Series Title: Algebras and applications, 11.
Responsibility: Manfred Knebusch ; translated by Thomas Unger.
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Abstract:

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. This  Read more...

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From the reviews: "In the present book Knebusch develops a theory of specialization covering all the situations occurring by combining the cases when the characteristic of the field L is equal or Read more...

 
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