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二次型的代数和几何理论（影印版）

样章
作者：
Richard Elman, Nikita Karpenko, Alexander Merkurjev
定价：
169.00元
ISBN：
978-7-04-053495-5
版面字数：
730.000千字
开本：
16开
全书页数：
暂无
装帧形式：
精装
重点项目：
暂无
出版时间：
2020-04-22
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
代数几何学
暂无
  • 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(<p)
      • 86. The Chow ring of Gr(y?) in the split case
      • 87. The Chow ring of Gr(<^) in the general case
      • 88. The invariant J(y>)
      • 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

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