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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
Table of Contents
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Front/Back Matter
Chapters
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