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Quadratic Forms with Applications to Algebraic Geometry and Topology

Author: Albrecht Pfister
Publisher: Cambridge : Cambridge University Press, 1995.
Series: London Mathematical Society lecture note series, no. 217.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
A gem of a book bringing together 30 years worth of results that are certain to interest anyone whose research touches on quadratic forms.
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Albrecht Pfister
ISBN: 9780511526077 0511526075 9780521467551 0521467551 9781107366985 1107366984
OCLC Number: 776978894
Notes: Title from publishers bibliographic system (viewed 22 Dec 2011).
Description: 1 online resource (188 pages).
Contents: Cover --
Half-title --
Title --
Copyright --
Contents --
Preface --
Chapter 1. The Representation Theorems of Cassels --
1. Preliminaries on Quadratic Forms --
2. The Main Theorem --
3. The Subform Theorem --
4. Appendix: The case char K = 2 --
Chapter 2. Multiplicative Quadratic Forms --
1. The Theorem of Witt --
2. The Multiplicative Forms --
3. Classification of Multiplicative Forms. Consequences for W(K) --
4. Appendix: The case char K = 2 --
Chapter 3. The Level of Fields, Rings, and Topological Spaces --
1. The Level of Fields --
2. The Level of Rings. 3. The Level of Topological Spaces --
Chapter 4. Hilbert's Homogeneous Nullstellensatz forp-fields and Applications to Topology --
1. The Nullstellensatz --
2. The Borsuk-Ulam and Brouwer Theorems --
Chapter 5. Tsen-Lang Theory for Cf-fields --
1. The Main Theorems --
2. Some Related Results and Conjectures --
Chapter 6. Hilbert's 17th Problem --
1. Preliminaries on Ordered and Real Fields --
2. Artin's Solution and other Qualitative Results --
3. Quantitative Bounds for the Number of Squares --
Chapter 7. The Pythagoras Number --
1. Results for Fields --
2. Results for Rings. Chapter 8. The it-invariant --
1. Definitions and Examples --
2. The Filtration of Elman and Lam --
3. Various Further Results --
4. Appendix: The case char K = 2 --
Chapter 9. Systems of Quadratic Forms --
1. Some General Phenomena --
2. Leep's Theorem --
3. Systems over Real Fields --
Chapter 10. The Level of Projective Spaces --
1. Algebraic and Topological Preliminaries --
2. The Level of RP2m-1 --
3. Estimates for the Level of Complex Projective Spaces --
Bibliography --
List of Symbols --
Index.
Series Title: London Mathematical Society lecture note series, no. 217.
Responsibility: Albrecht Pfister.

Abstract:

This volume has grown out of lectures given by Professor Pfister over many years. The emphasis here is placed on results about quadratic forms that give rise to interconnections between number  Read more...

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'A very readable complement to the standard treatments.' Mathematica

 
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