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出版社:高等教育出版社 ISBN:9787040534955 商品編碼:10027397633064 品牌:文軒 出版時間:2020-04-01 代碼:169 作者:李察·埃爾曼,尼基塔·卡彭科,亞
" 作 者:(美)李察·埃爾曼,(法)尼基塔·卡彭科,(美)亞歷山大·梅爾庫耶夫 著 定 價:169 出 版 社:高等教育出版社 出版日期:2020年04月01日 頁 數:456 裝 幀:精裝 ISBN:9787040534955 ●Introduction Part 1.Classical theory of symmetric bilinear forms and quadratic forms Chapter Ⅰ.Bilinear Forms 1.Foundations 2.The Witt and Witt-Grothendieck 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 Pfster forms Chapter Ⅵ.u-invariants 36.The u-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.K-homology groups 53.Euler classes and projective bundle theorem 54.Chern classes 55.Gysin and pull-back homomorphisms 56.K-cohomology ring of smooth schemes Chapter Ⅹ.Chow Groups 57.Definition of Chow groups 58.Segre and Chern classes Chapter Ⅺ.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 O 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(ψ) 86.The Chow ring of Gr(ψ)in the split case 87.The Chow ring of Gr(ψ)in the general case …… 本書是對二次型代數理論的全面研究,從古典理論到近期新進展,包括從未出版過的結果和證明。本書采用了代數幾何學的觀點,包括特征2的域上的二次型理論,證明盡可能是特征獨立的。對於一些結果,既給出了經典證明,又給出了幾何證明。本書第一部分包括經典的二次型和雙線性型代數理論,回答了該理論發展初期提出的許多問題。在代數幾何學隻有一門基礎課程的假設下,本書第二部分介紹了代數幾何學中必要的附加專題,包括Chow群理論、Chow運動和Steenrod運算。這些專題在第三部分中被用來發展二次型的現代幾何理論。
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