作者：MarcLevine
页数：515
出版社：高等教育出版社
出版日期：2020
ISBN：9787040535013
电子书格式：pdf/epub/txt
内容简介
《混合 Motives（影印版）》将motives理论的基本构造和motives上同调的有关结果相结合，形成更为显式的构造。理解这项工作需要先了解代数几何的基本知识。 作者构造并描述了任意基础概形上混合motives的三角范畴。大多数上同调的经典构造是在motives环境中描述的，包括高阶K-理论的陈类，逆紧映射的前推，Riemann-Roch定理，对偶，以及相关的motives同调，具有紧支撑的Borel-Moore同调和上同调。 《混合 Motives（影印版）》适合对代数几何和K-理论感兴趣的研究生和数学研究人员阅读。
本书特色
本书将motives理论的基本构造和motives上同调的有关结果相结合，形成更为显式的构造。理解这项工作需要先了解代数几何的基本知识。作者构造并描述了任意基础概形上混合motives的三角范畴。大多数上同调的经典构造是在motives环境中描述的，包括高阶K-理论的陈类，逆紧映射的前推，Riemann-Roch定理，对偶，以及相关的motives同调，具有紧支撑的Borel-Moore同调和上同调。本书适合对代数几何和K-理论感兴趣的研究生和数学研究人员阅读。
目录
Preface
Part Ⅰ.Motives
Introduction: Part Ⅰ
Chapter Ⅰ.The Motivic Category
1.The motivic DG category
2.The triangulated motivic category
3.Structure of the motivic categories
Chapter Ⅱ.Motivic Cohomology and Higher Chow Groups
1.Hypercohomology in the motivic category
2.Higher Chow groups
3.The motivic cycle map
Chapter Ⅲ.K-Theory and Motives
1.Chern classes
2.Push-forward
3.Riemann-Roch
Chapter Ⅳ.Homology, Cohomology, and Duality
1.Duality
2.Classical constructions
3.Motives over a perfect field
Chapter Ⅴ.Realization of the Motivic Category
1.Realization for geometric cohomology
2.Concrete realizations
Chapter Ⅵ.Motivic Constructions and Comparisons
1.Motivic constructions
2.Comparison with the category DMom(k)
Appendix A.Equi-dimensional Cycles
1.Cycles over a normal scheme
2.Cycles over a reduced scheme
Appendix B.K-Theory
1.K-theory of rings and schemes
2.K-theory and homology
Part Ⅱ.Categorical Algebra
Introduction: Part Ⅱ
Chapter Ⅰ.Symmetric Monoidal Structures
1.Foundational material
2.Constructions and computations
Chapter Ⅱ.DG Categories and Triangulated Categories
1.Differential graded categories
2.Complexes and triangulated categories
3.Constructions
Chapter Ⅲ.Simplicial and Cosimplicial Constructions
1.Complexes arising from simplicial and cosimplicial objects
2.Categorical cochain operations
3.Homotopy limits
Chapter Ⅳ.Canonical Models for Cohomology
1.Sheaves, sites, and topoi
2.Canonical resolutions
Bibliography
Subject Index
Index of Notation
Part Ⅰ.Motives
Introduction: Part Ⅰ
Chapter Ⅰ.The Motivic Category
1.The motivic DG category
2.The triangulated motivic category
3.Structure of the motivic categories
Chapter Ⅱ.Motivic Cohomology and Higher Chow Groups
1.Hypercohomology in the motivic category
2.Higher Chow groups
3.The motivic cycle map
Chapter Ⅲ.K-Theory and Motives
1.Chern classes
2.Push-forward
3.Riemann-Roch
Chapter Ⅳ.Homology, Cohomology, and Duality
1.Duality
2.Classical constructions
3.Motives over a perfect field
Chapter Ⅴ.Realization of the Motivic Category
1.Realization for geometric cohomology
2.Concrete realizations
Chapter Ⅵ.Motivic Constructions and Comparisons
1.Motivic constructions
2.Comparison with the category DMom(k)
Appendix A.Equi-dimensional Cycles
1.Cycles over a normal scheme
2.Cycles over a reduced scheme
Appendix B.K-Theory
1.K-theory of rings and schemes
2.K-theory and homology
Part Ⅱ.Categorical Algebra
Introduction: Part Ⅱ
Chapter Ⅰ.Symmetric Monoidal Structures
1.Foundational material
2.Constructions and computations
Chapter Ⅱ.DG Categories and Triangulated Categories
1.Differential graded categories
2.Complexes and triangulated categories
3.Constructions
Chapter Ⅲ.Simplicial and Cosimplicial Constructions
1.Complexes arising from simplicial and cosimplicial objects
2.Categorical cochain operations
3.Homotopy limits
Chapter Ⅳ.Canonical Models for Cohomology
1.Sheaves, sites, and topoi
2.Canonical resolutions
Bibliography
Subject Index
Index of Notation
