前辅文
Introduction
Part 1. Classical theory of symmetric bilinear forms and quadratic forms
Chapter I. Bilinear Forms
1. Foundations
2. The Witt and Witt-Grot hendieck rings of symmetric bilinear forms
3. Chain equivalence
4. Structure of the Witt ring
5. The Stiefel-Whitney map
6. Bilinear Pfister forms
Chapter II. Quadratic Forms
7. Foundations
8. Witt's Theorems
9. Quadratic Pfister forms I
10. Totally singular forms
11. The Clifford algebra
12. Binary quadratic forms and quadratic algebras
13. The discriminant
14. The Clifford invariant
15. Chain p-equivalence of quadratic Pfister forms
16. Cohomological invariants
Chapter III. Forms over Rational Function Fields
17. The Cassels-Pfister Theorem
18. Values of forms
19. Forms over a discrete valuation ring
20. Similarities of forms
21. An exact sequence for W(F(t))
Chapter IV. Function Fields of Quadrics
22. Quadrics
23. Quadratic Pfister forms II
24. Linkage of quadratic forms
25. The submodule Jn(F)
26. The Separation Theorem
27. A further characterization of quadratic Pfister forms
28. Excellent quadratic forms
29. Excellent field extensions
30. Central simple algebras over function fields of quadratic forms
Chapter V. Bilinear and Quadratic Forms and Algebraic Extensions
31. Structure of the Witt ring
32. Addendum on torsion
33. The total signature
34. Bilinear and quadratic forms under quadratic extensions
35. Torsion in In(F) and torsion Pfister forms
Chapter VI. u-invariants
36. The iz-invariant
37. The u-invariant for formally real fields
38. Construction of fields with even u-invariant
39. Addendum: Linked fields and the Hasse number
Chapter VII. Applications of the Milnor Conjecture
40. Exact sequences for quadratic extensions
41. Annihilators of Pfister forms
42. Presentation of In(F)
43. Going down and torsion-freeness
Chapter VIII. On the Norm Residue Homomorphism of Degree Two
44. The main theorem
45. Geometry of conic curves
46. Key exact sequence
47. Hilbert Theorem 90 for K2
48. Proof of the main theorem
Part 2. Algebraic cycles
Chapter IX. Homology and Cohomology
49. The complex C* (X)
50. External products
51. Deformation homomorphisms
52. if-homology groups
53. Euler classes and projective bundle theorem
54. Chern classes
55. Gysin and pull-back homomorphisms
56. if-cohomology ring of smooth schemes
Chapter X. Chow Groups
57. Definition of Chow groups
58. Segre and Chern classes
Chapter XL Steenrod Operations
59. Definition of the Steenrod operations
60. Properties of the Steenrod operations
61. Steenrod operations for smooth schemes
Chapter XII. Category of Chow Motives
62. Correspondences
63. Categories of correspondences
64. Category of Chow motives
65. Duality
66. Motives of cellular schemes
67. Nilpotence Theorem
Part 3. Quadratic forms and algebraic cycles
Chapter XIII. Cycles on Powers of Quadrics
68. Split quadrics
69. Isomorphisms of quadrics
70. Isotropic quadrics
71. The Chow group of dimension 0 cycles on quadrics
72. The reduced Chow group
73. Cycles on X2
Chapter XIV. The Izhboldin Dimension
74. The first Witt index of subforms
75. Correspondences
76. The main theorem
77. Addendum: The Pythagoras number
Chapter XV. Application of Steenrod Operations
78. Computation of Steenrod operations
79. Values of the first Witt index
80. Rost correspondences
81. On the 2-adic order of higher Witt indices, I
82. Holes in In
83. On the 2-adic order of higher Witt indices, II
84. Minimal height
Chapter XVI. The Variety of Maximal Totally Isotropic Subspaces
85. The variety Gr()
89. Steenrod operations on Ch(Gr (<￡>))
90. Canonical dimension
Chapter XVII. Motives of Quadrics
91. Comparison of some discrete invariants of quadratic forms
92. The Nilpotence Theorem for quadrics
93. Criterion of isomorphism
94. Indecomposable summands
Appendices
95. Formally real fields
96. The space of orderings
97. Cn-fields
98. Algebras
99. Galois cohomology
100. Milnor if-theory of fields
101. The cohomology groups Hn^(F, Z/raZ)
102. Length and Herbrand index
103. Places
104. Cones and vector bundles
105. Group actions on algebraic schemes
Bibliography
Notation
Terminology
