导语

  

内容提要

  

    20世纪20年代，Springer出版了Grundlehren der Mathematicschen Wissenschaften专著系列丛书，各卷有不同作者撰写，内容独立成册，其中有些高等经典教材广受好评。为了满足不断涌现的新一代研究生和科研人员的需求，Springer将这类图书重新出版，形成了新的系列“经典数学”丛书（Classics in Mathematics），O.T.欧米拉著的《二次型导论(英文版)》正是选自该丛书，本书虽然不是一部内容浅显的教科书，但二次型理论阐述清晰明了，独具特色。

Prerequisites and Notation
Part One  Arithmetic Theory of Fields
  Chapter I. Valuated Fields
    11. Valuations
    12. Arehimedean valuations
    13. Non-archimedean valuations
    14. Prolongation of a complete valuation to a finite extension
    15. Prolongat/on of any valuation to a finite separable extension . .
    16. Discrete valuations
  Chapter II. Dedekind Theory of Ideals
    21. Dedekind axioms for S
    22. Ideal theory
    23. Extens/on fields
  Chapter III. Fields of Number Theory
    31. Rational global fields
    32. Local fields
    33. Global fields
Part Two  Abstract Theory of Quadratic Forms
  Chapter IV. Quadratic Forms and the O~ogonal Group
    41. Forms, matrices and spaces
    42. Quadratic spaces
    43. Special subgroups of O.(V)
  Chapter V. The Algebras of Quadratic Forms
    Sl. Tensor products
    52. Wedderburn's theorem on central simple algebras
    53. Extending the field of scalars
    54, The Clifford algebra
    55. The spinor norm
    56. Special subgroups of O,(V)
    57. Quaternion algebras
    58. The Hasse algebra
Part Three  Arithmetic Theory of Quadratic Forms over Fields
  Chapter VI. The Equivalence of Quadratic Forms
    61. Complete archimedean fields
    62. Finite fields
    63. Local fields
    64. Global notation
    68. Squares and norms in giobal fields
    66. Quadratic forms over global fields
  Chapter VII. Hilbert's Reciprocity Law
    71. Proof of the reciprocity law
    72. Existence of forms with prescribed local behavior
    73. The quadratic reciprocity law
Part Four  Arithmetic Theory of ~uadratie Forms over Rings
  Chapter VIII. Quadratic Forms over Dedekind Domains
    81. Abstract lattices
    82. Lattices in quadratic spaces
  Chapter IX. Integral Theory of Quadratic Forms over Local Fields
    91. Generalities
    92. Classification of lattices over non-dyadic fields
    93. Classification of lattices over dyadic fields
    94. Effective determination of the invariants
    95. Special subgroups of 0. (V)
  Chapter X. Integral Theory of Quadratic Forms over Global Fields
    101. Elementary properties of the orthogonal group over arithmetic fields
    102. The genus and the spinor genus
    103. Finiteness of class number
    104. The class and the spinor genus in the indefinite case
    10S. The indecomposable splitting of a definite lattice
    106. Definite unimodular lattices over the rational integers
Bibliography
Index