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数域的上同调 英文 第2版2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

数域的上同调 英文 第2版
  • （德）J.诺伊基希；（德）A.施密特；（德）K.温伯格著 著
  • 出版社： 北京;西安：世界图书出版公司
  • ISBN：7519219674
  • 出版时间：2016
  • 标注页数：826页
  • 文件大小：118MB
  • 文件页数：842页
  • 主题词：数域－英文；上同调－英文

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图书目录

Algebraic Theory1

Chapter Ⅰ：Cohomology of Profinite Groups3

1．Profinite Spaces and Profinite Groups3

2．Definition of the Cohomology Groups12

3．The Exact Cohomology Sequence25

4．The Cup-Product36

5．Change of the Group G45

6．Basic Properties60

7．Cohomology of Cyclic Groups74

8．Cohomological Triviality80

9．Tate Cohomology of Profinite Groups83

Chapter Ⅱ：Some Homological Algebra97

1．Spectral Sequences97

2．Filtered Cochain Complexes101

3．Degeneration of Spectral Sequences107

4．The Hochschild-Serre Spectral Sequence111

5．The Tate Spectral Sequence120

6．Derived Functors127

7．Continuous Cochain Cohomology136

Chapter Ⅲ：Duality Properties of Profinite Groups147

1．Duality for Class Formations147

2．An Alternative Description of the Reciprocity Homomorphism164

3．Cohomological Dimension171

4．Dualizing Modules181

5．Projective pro-c-groups189

6．Profinite Groups of scd G=2202

7．Poincaré Groups210

8．Filtrations220

9．Generators and Relations224

Chapter Ⅳ：Free Products of Profinite Groups245

1．Free Products245

2．Subgroups of Free Products252

3．Generalized Free Products256

Chapter Ⅴ：Iwasawa Modules267

1．Modules up to Pseudo-Isomorphism268

2．Complete Group Rings273

3．Iwasawa Modules289

4．Homotopy of Modules301

5．Homotopy Invariants of Iwasawa Modules312

6．Differential Modules and Presentations321

Arithmetic Theory335

Chapter Ⅵ：Galois Cohomology337

1．Cohomology of the Additive Group337

2．Hilbert's Satz 90343

3．The Brauer Group349

4．The Milnor K-Groups356

5．Dimension of Fields360

Chapter Ⅶ：Cohomology of Local Fields371

1．Cohomology of the Multiplicative Group371

2．The Local Duality Theorem378

3．The Local Euler-Poincaré Characteristic391

4．Galois Module Structure of the Multiplicative Group401

5．Explicit Determination of Local Galois Groups409

Chapter Ⅷ：Cohomology of Global Fields425

1．Cohomology of the Idè1e Class Group425

2．The Connected Component of Ck443

3．Restricted Ramification452

4．The Global Duality Theorem466

5．Local Cohomology of Global Galois Modules472

6．Poitou-Tate Duality480

7．The Global Euler-PoincaréCharacteristic503

8．Duality for Unramified and Tamely Ramified Extensions513

Chapter Ⅸ：The Absolute Galois Group of a Global Field521

1．The Hasse Principle522

2．The Theorem of Grunwald-Wang536

3．Construction of Cohomology Classes543

4．Local Galois Groups in a Global Group553

5．Solvable Groups as Galois Groups557

6．？afarevi？'s Theorem574

Chapter Ⅹ：Restricted Ramification599

1．The Function Field Case602

2．First Observations on the Number Field Case618

3．Leopoldt's Conjecture624

4．Cohomology of Large Number Fields642

5．Riemann's Existence Theorem647

6．The Relation between 2 and ∞656

7．Dimension of Hi(G？,Z/pZ)666

8．The Theorem of Kuz'min678

9．Free Product Decomposition of Gs(p)686

10．Class Field Towers697

11．The Profinite Group Gs706

Chapter Ⅺ：Iwasawa Theory of Number Fields721

1．The Maximal Abelian Unramified p-Extension of k∞722

2．Iwasawa Theory for p-adic Local Fields731

3．The Maximal Abelian p-Extension of k∞ Unramified Outside S735

4．Iwasawa Theory for Totally Real Fields and CM-Fields751

5．Positively Ramified Extensions763

6．The Main Conjecture771

Chapter Ⅻ：Anabelian Geometry785

1．Subgroups of Gk785

2．The Neukirch-Uchida Theorem791

3．Anabelian Conjectures798

Literature805

Index821

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