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The Algebraic and Geometric Theory of Quadratic Forms

About this Title

Richard Elman, University of California, Los Angeles, CA, Nikita Karpenko, Université Pierre et Marie Curie - Paris 6, Paris, France and Alexander Merkurjev, University of California, Los Angeles, CA

Publication: Colloquium Publications
Publication Year: 2008; Volume 56
ISBNs: 978-0-8218-4329-1 (print); 978-1-4704-3202-7 (online)
DOI: https://doi.org/10.1090/coll/056
MathSciNet review: MR2427530
MSC: Primary 11Exx; Secondary 11-02, 11E04, 11E81, 14C15, 14C25

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Table of Contents

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Front/Back Matter

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Chapters

• Introduction

Classical theory of symmetric bilinear forms and quadratic forms

• Chapter 1. Bilinear forms
• Chapter 2. Quadratic forms
• Chapter 3. Forms over rational function fields
• Chapter 4. Function fields of quadrics
• Chapter 5. Bilinear and quadratic forms and algebraic extensions
• Chapter 6. $u$-invariants
• Chapter 7. Applications of the Milnor conjecture
• Chapter 8. On the norm residue homomorphism of degree two

Algebraic cycles

• Chapter 9. Homology and cohomology
• Chapter 10. Chow groups
• Chapter 11. Steenrod operations
• Chapter 12. Category of Chow motives

Quadratic forms and algebraic cycles

• Chapter 13. Cycles on powers of quadrics
• Chapter 14. The Izhboldin dimension
• Chapter 15. Application of Steenrod operations
• Chapter 16. The variety of maximal totally isotropic subspaces
• Chapter 17. Motives of quadrics
• Appendices