Higher algebraic K-theory: an overview
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1992
|
| Schriftenreihe: | Lecture notes in mathematics
1491 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | IX, 164 S. |
| ISBN: | 3540550070 0387550070 |
Internformat
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| 245 | 1 | 0 | |a Higher algebraic K-theory |b an overview |c E. Lluis-Puebla ... |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1992 | |
| 300 | |a IX, 164 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1491 | |
| 500 | |a Literaturangaben | ||
| 650 | 4 | |a K-théorie - Congrès | |
| 650 | 4 | |a K-theory |v Congresses | |
| 650 | 0 | 7 | |a Algebraische K-Theorie |0 (DE-588)4141839-6 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4143413-4 |a Aufsatzsammlung |2 gnd-content | |
| 655 | 7 | |0 (DE-588)1071861417 |a Konferenzschrift |2 gnd-content | |
| 689 | 0 | 0 | |a Algebraische K-Theorie |0 (DE-588)4141839-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Lluis-Puebla, Emilio |e Sonstige |4 oth | |
| 830 | 0 | |a Lecture notes in mathematics |v 1491 |w (DE-604)BV000676446 |9 1491 | |
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Datensatz im Suchindex
| _version_ | 1805082730975723520 |
|---|---|
| adam_text |
Contents
Introduction to Algebraic if Theory
(Emilio LMs Puebla) 1
I. Some Homological Algebra 2
1.1. Modules 2
1.2. Resolutions and Homology . 5
1.3. Torsion and Extension Functors 9
II. Cohomology of Groups 16
11.1. G Modules and the (Co)Homology of a Group 16
11.2. Hi(G,N) and Hl(G,N) 19
11.3. H2(G, N) and Some Calculations 22
III. Classical Algebraic if Theory 25
111.1. K0A 25
111.2. KiA 26
111.3. K2A 28
Bibliography and References 30
Introduction to Algebraic K Theory and Cyclic Homology
{Jean Louis Loday) 31
1. Hochschild Homology and Rational Cyclic Homology 33
2. The Proof of K+= HCn X 34
3. Integral Cyclic Homology [L Q] 38
Operations in Cyclic Homology 41
Action of a Derivation 43
4. Cyclic Homology of Truncated Polynomial Rings 43
5. Quillen's Plus Construction and Kn ([Q], [LI]) 44
6. Ki, K2 and #3 48
6.1. Ki(A) 48
6.2. K2(A) 49
6.5. K3(A) 50
7. Product and Milnor if Theory 51
8. if Theory of Nilpotent Ideals 52
References 53
Comparing Algebraic and Topological if Theory
(Henri Gillet) 55
1. What is Algebraic if Theory? 57
2. Topological A' Theory 60
2.1. Vector Bundles 60
2.2. Sheaves of Sections 62
VIII
2.3. Properties of the Category of Vector Bundles 63
2.4 K theory of compact spaces 65
2.5. Higher /( Theory 66
2.6. The Atiyah Hirzebruch Spectral Sequence 67
2.7. Chern Classes 67
3. Ko of Schemes 68
3.1. Affine Schemes 68
3.2. Schemes 69
3.3. Algebraic bundles 70
3.4. #0 of Schemes 72
3.5. Ko and Algebraic Cycles 73
4. Higher /( Theory of Varieties and Schemes 74
4.1 74
4.2. The Q construction 75
Properties of K»M 76
4.3. /( theory of Rings and Schemes 78
4.4. The + Construction 79
4.5. Examples and Computations 80
4.6. Connections with Geometry and Arithmetic 81
5. The Map From K** to /(t°op 81
5.1. Algebraic vs. Topological Bundles 82
5.2. Construction of r]° 83
5.3 83
5.4. Basic Ideas of Hodge Theory 84
5.5. Hodge Theory and r;0 85
6. The Map From Higher Algebraic /( Theory to Topological /( Theory 87
6.1. The Affine Case 87
6.2. The Quasi projective Case 88
6.3. The Image of t] 89
7 91
7.1. /( Theory with Coefficients 91
7.2. Divisor Class Groups 94
7.3. Generalized Jacobians and the Transfer on /( Theory 94
7.4. Suslin's Rigidity Theorem 96
References 97
Algebraic /( Theory of the Integers
(Christophe Soule) 100
I. Introduction: /( Theory of Integers and Values of Zeta Functions . 101
1. /( Theory of 2 101
2. Bernoulli Numbers 102
3. Values of the Riemann Zeta Function 103
II. Finite Generation of the/( Theory of Integers 107
1. The/( theory of 2 107
IX
2. Finite generation 108
3. Reduction Theory 109
4. Congruence Subgroups 110
5. A Good Subspace Ill
6. Conclusion 112
III. The X Theory of Complex Numbers With Finite Coefficients 112
1. Statement of the Result 113
2. Description of a Fiber . 114
3. if Theory of Hensel Rings 116
4. The Universal Chain Construction 117
IV. Chern Classes of Discrete Groups 119
1. Chern Classes for the Discrete Group GLN (C) 120
2. Chern Classes for the Discrete Group GLN(Z) 121
V. Etale Cohomology 123
1. Denominators 123
2. Numerators 127
3. Conclusions 129
References 130
Applications of Group Cohomology to Bilinear Forms
(Victor Snaith) 133
Introduction 133
I. Abelian Cohomology of Groups 134
II 138
III. Non abelian Cohomology of Groups 143
IV 147
V 151
VI 154
VII. Orthogonal Local Root Numbers 157
References 164 |
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| isbn | 3540550070 0387550070 |
| language | English |
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| physical | IX, 164 S. |
| publishDate | 1992 |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Higher algebraic K-theory an overview E. Lluis-Puebla ... Berlin [u.a.] Springer 1992 IX, 164 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1491 Literaturangaben K-théorie - Congrès K-theory Congresses Algebraische K-Theorie (DE-588)4141839-6 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content (DE-588)1071861417 Konferenzschrift gnd-content Algebraische K-Theorie (DE-588)4141839-6 s DE-604 Lluis-Puebla, Emilio Sonstige oth Lecture notes in mathematics 1491 (DE-604)BV000676446 1491 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003407267&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Higher algebraic K-theory an overview Lecture notes in mathematics K-théorie - Congrès K-theory Congresses Algebraische K-Theorie (DE-588)4141839-6 gnd |
| subject_GND | (DE-588)4141839-6 (DE-588)4143413-4 (DE-588)1071861417 |
| title | Higher algebraic K-theory an overview |
| title_auth | Higher algebraic K-theory an overview |
| title_exact_search | Higher algebraic K-theory an overview |
| title_full | Higher algebraic K-theory an overview E. Lluis-Puebla ... |
| title_fullStr | Higher algebraic K-theory an overview E. Lluis-Puebla ... |
| title_full_unstemmed | Higher algebraic K-theory an overview E. Lluis-Puebla ... |
| title_short | Higher algebraic K-theory |
| title_sort | higher algebraic k theory an overview |
| title_sub | an overview |
| topic | K-théorie - Congrès K-theory Congresses Algebraische K-Theorie (DE-588)4141839-6 gnd |
| topic_facet | K-théorie - Congrès K-theory Congresses Algebraische K-Theorie Aufsatzsammlung Konferenzschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003407267&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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