Galois cohomology of algebraic number fields: With two appendices by Helmut Koch and Thomas Zink
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin
Dt. Verl. d. Wiss.
1978
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Enth. außerdem u.a.: On p-extensions with given ramification / by Helmut Koch |
| Physical Description: | 145 S. |
Staff View
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| 245 | 1 | 0 | |a Galois cohomology of algebraic number fields |b With two appendices by Helmut Koch and Thomas Zink |
| 264 | 1 | |a Berlin |b Dt. Verl. d. Wiss. |c 1978 | |
| 300 | |a 145 S. | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Introduction 11
Logical dependence of the theorems 12
1. Formulation of results 13
1.1. Notation 13
1.2. Local results 14
1.3. Formulation of Tate s Theorem 15
1.4. First remarks and plan of proof 16
2. The eohomologieal dimension of G 17
2.1. The cohomology of the S units 17
2.2. The usual cohomological dimension of G 20
2.3. Malleable groups 23
2.4. On the strict cohomological dimension of G 27
2.5. Modification of the class formation (G, Cs) and the universal norms of the iS
idele class group 28
3. The global Euler Poineare characteristic 30
3.1. Formulation of the theorem . . 30
3.2. Proof step 1: Multiplicativity 30
3.3. Proof step 2: Behaviour in the case of induced modules 31
3.4. Proof step 3: Reduction to the case „!/ = ,Hp 32
3.5. Proof step 4: Calculation of the Euler Poincare characteristic for /ip 34
3.6. End of the proof 35
4. The Tate pairing 36
4.1. The homology of profinite groups r 36
4.2. The proposition concerning Tate s pairing 40
4.3. On the module dualisant of a number field 44
4.4. Once again on the strict cohomological dimension of G 46
5. Proof of Tate s Theorem 3.1 51
5.1. The cohomology of Horn (31, Js) 51
5.2. Half of the Tate sequence 53
5.3. Explicit description of the pairing from Theorem 3.1(a) 55
5.4. Proof of Tate s Theorem 3.1(c) 56
5.5. The exactness of the Tate sequence in the middle term 57
5.6. On the functorial behaviour of the Tate sequence 59
6 Contents
6. On the maximal pro p factor group of G 59
6.1. First remarks 39
6.2. Twisted action 60
6.3. Proof of Proposition 22 61
7. Remarks concerning the kernel of the map ax 63
7.1. A general method for determining Ker1 (kg, M) 63
7.2. An algebraic consideration tio
7.3. Construction of non trivial kernels 66
8. On the Scholz Reichardt Xeukireh Proposition 68
g.l. The central embedding problem for groups 68
8.2. The central embedding problem for number fields 69
8.3. The local case 69
8.4. The global case 70
9. Quantitative statements in the simple case of the constructional problem for
finite p groups 73
9.1. Introductory remarks 73
9.2. The Abelian case 73
9.3. The simple case of a p group — first remarks 75
9.4. The simple case of a ^ group — local questions 77
9.5. The simple case of a y group — global questions 79
9.6. The simple case of a ^ group — analytical part 80
9.7. The simple case of a ^ group — independence of the sum of constants .... 83
9.8. Examples 85
Bibliography 86
Appendix 1. On ^ extensions with given ramification (H. Koch)
1. Representations of pro j» groups by generators and relations 89
1.1. The generator rank 89
1.2. Relation systems 90
2. The group algebra of a pro p group 94
2.1. Definition and basic properties of the completed group algebra 94
2.2. Discrete and compact G modules 96
2.3. Characterisation of pro p groups with dimension 2 96
2.4. Filiations 98
2.5. The completed group ring of a free pro y group 100
2.6. Lazard filtrations 101
2.7. The theorem of Golod Shafabewich 102
2.8. The structure of the relations and the cup product 106
3. The maximal jj extension of a p adie number field 109
4. The maximal / extensioii with given ramification 112
Contents 7
5. Generator rank . . . 117
(!. The case fc=Q 119
7. The 2 class field tower of a quadratic number field 122
Bibliography 125
Appendix 2. Etale cohomology and duality in number fields (Th. Zink)
1. Etale topology of algebraic number fields 127
2. Cohomology 131
3. Artin Verdier duality 137
Bibliography 145
|
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| id | DE-604.BV002257939 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:42:54Z |
| institution | BVB |
| language | English |
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| physical | 145 S. |
| psigel | TUB-nveb |
| publishDate | 1978 |
| publishDateSearch | 1978 |
| publishDateSort | 1978 |
| publisher | Dt. Verl. d. Wiss. |
| record_format | marc |
| spelling | Haberland, Klaus Verfasser aut Galois cohomology of algebraic number fields With two appendices by Helmut Koch and Thomas Zink Berlin Dt. Verl. d. Wiss. 1978 145 S. txt rdacontent n rdamedia nc rdacarrier Enth. außerdem u.a.: On p-extensions with given ramification / by Helmut Koch Algebraischer Zahlkörper (DE-588)4068537-8 gnd rswk-swf Zahlkörper (DE-588)4067273-6 gnd rswk-swf Galois-Kohomologie (DE-588)4019172-2 gnd rswk-swf Algebraischer Zahlkörper (DE-588)4068537-8 s Galois-Kohomologie (DE-588)4019172-2 s DE-604 Zahlkörper (DE-588)4067273-6 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001483832&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Haberland, Klaus Galois cohomology of algebraic number fields With two appendices by Helmut Koch and Thomas Zink Algebraischer Zahlkörper (DE-588)4068537-8 gnd Zahlkörper (DE-588)4067273-6 gnd Galois-Kohomologie (DE-588)4019172-2 gnd |
| subject_GND | (DE-588)4068537-8 (DE-588)4067273-6 (DE-588)4019172-2 |
| title | Galois cohomology of algebraic number fields With two appendices by Helmut Koch and Thomas Zink |
| title_auth | Galois cohomology of algebraic number fields With two appendices by Helmut Koch and Thomas Zink |
| title_exact_search | Galois cohomology of algebraic number fields With two appendices by Helmut Koch and Thomas Zink |
| title_full | Galois cohomology of algebraic number fields With two appendices by Helmut Koch and Thomas Zink |
| title_fullStr | Galois cohomology of algebraic number fields With two appendices by Helmut Koch and Thomas Zink |
| title_full_unstemmed | Galois cohomology of algebraic number fields With two appendices by Helmut Koch and Thomas Zink |
| title_short | Galois cohomology of algebraic number fields |
| title_sort | galois cohomology of algebraic number fields with two appendices by helmut koch and thomas zink |
| title_sub | With two appendices by Helmut Koch and Thomas Zink |
| topic | Algebraischer Zahlkörper (DE-588)4068537-8 gnd Zahlkörper (DE-588)4067273-6 gnd Galois-Kohomologie (DE-588)4019172-2 gnd |
| topic_facet | Algebraischer Zahlkörper Zahlkörper Galois-Kohomologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001483832&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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