Galois theory of p-extensions:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English German |
| Published: |
Berlin [u.a.]
Springer
2002
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| Series: | Springer monographs in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 190 S. graph. Darst. |
| ISBN: | 3540436294 |
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Record in the Search Index
| _version_ | 1804129294690025472 |
|---|---|
| adam_text | HELMUT KOCH GALOIS THEORY OFP-EXTENSIONS SPRINGER CONTENTS INTRODUCTION
1 1. PROFINITE GROUPS 3 1.1 PROJECTIVE LIMITS OF GROUPS AND RINGS 3 1.2
PROFINITE GROUPS 7 1.3 SUBGROUPS AND QUOTIENT GROUPS 9 1.4 ABELIAN
PROFINITE GROUPS, PONTRYAGIN S DUALITY THEORY 10 1.5 .DISCRETE MODULES
10 1.6 THE CATEGORY C 12 1.7 INDUCTIVE LIMITS IN C 13 2. GALOIS THEORY
OF INFINITE ALGEBRAIC EXTENSIONS 17 2.1 THE GALOIS GROUP OF INFINITE
EXTENSIONS 17 2.2 THE MAIN THEOREM OF GALOIS THEORY 19 3. COHOMOLOGY OF
PROFINITE GROUPS 21 3.1 DEFINITION OF COHOMOLOGY GROUPS 21 3.2 GROUP
EXTENSIONS 24 3.3 DIMENSION SHIFTING 24 3.4 SHAPIRO S LEMMA 28 3.5
RESTRICTION AND CORESTRICTION 28 3.6 THE TRANSFER 29 3.7 INFLATION AND
TRANSGRESSION 30 3.8 INDUCTIVE LIMITS OF COHOMOLOGY GROUPS 35 3.9 CUP
PRODUCTS 37 4. FREE PRO-P GROUPS 41 4.1 CONSTRUCTION OF FREE PRO-P
GROUPS 41 4.2 THE MAGNUS GROUP ALGEBRA 42 4.3 ABELIAN PRO-P GROUPS 43
4.4 FIRST CHARACTERIZATION OF FREE PRO-P GROUPS 44 4.5 SECOND
CHARACTERIZATION OF FREE PRO-P GROUPS 47 XII CONTENTS 5. COHOMOLOGICAL
DIMENSION 49 5.1 DEFINITION OF COHOMOLOGICAL DIMENSION 49 5.2
EULER-POINCARE CHARACTERISTIC 50 6. PRESENTATION OF PRO-P GROUPS 53 6.1
THE GENERATOR RANK 53 6.2 RELATION SYSTEMS 54 7. GROUP ALGEBRAS OF PRO-P
GROUPS 59 7.1 COMPLETE GROUP ALGEBRAS 59 7.2 DISCRETE AND COMPACT
G-MODULES 60 7.3 PRO-P GROUPS OF DIMENSION 2 61 7.4 FILTRATIONS 64 7.5
COMPUTING WITH COMMUTATORS AND POWERS 66 7.6 GROUP RINGS OF FREE PRO-P
GROUPS 68 7.7 THE THEOREM OF GOLOD-SHAFAREVICH 69 7.8 RELATION STRUCTURE
AND CUP PRODUCT 72 8. RESULTS FROM ALGEBRAIC NUMBER THEORY 77 8.1
ALGEBRAIC NUMBER THEORY FOR INFINITE EXTENSIONS 77 8.2 NORMAL EXTENSIONS
77 8.3 THE FROBENIUS AUTOMORPHISM 79 8.4 LOCAL AND GLOBAL FIELDS 79 8.5
THE MULTIPLICATIVE GROUP OF A LOCAL FIELD 81 8.6 FINITE CLASS FIELD
THEORY 82 8.7 INFINITE CLASS FIELD THEORY 84 8.8 THE PRINCIPAL IDEAL
THEOREM 85 8.9 COHOMOLOGY OF THE FORMATION MODULE 87 8.10 COHOMOLOGY OF
THE MULTIPLICATIVE GROUP 89 8.11 NORM RESIDUE SYMBOL 90 9. THE MAXIMAL
P-EXTENSION 93 9.1 FIELDS OF CHARACTERISTIC P 93 9.2 FIELDS CONTAINING
THE P-TH ROOTS OF UNITY 94 9.3 FIELDS NOT CONTAINING THE P-TH ROOTS OF
UNITY 96 10. LOCAL FIELDS OF FINITE TYPE 9 9 10.1 THE CASE X{P) V 99
10.2 THE CASE X {P) = P, S{K) = 0 101 10.3 THE CASE X (P) = P, S{K) = 1
/* 103 11. GLOBAL FIELDS OF FINITE TYPE ILL 11.1 THE MAXIMAL P-EXTENSION
ILL 11.2 THE MAXIMAL P-EXTENSION WITH RESTRICTED RAMIFICATION 114 11.3
GENERATOR RANK V 119 CONTENTS XIII 11.4 EXPLICIT COMPUTATION OF
GENERATORS AND RELATIONS 122 11.5 THE STRUCTURE OF GS IN SPECIAL CASES
129 12. ON P-CLASS GROUPS AND P-CLASS FIELD TOWERS 133 12.1 A CRITERION
FOR CLASS NUMBER PRIME TO P 133 12.2 THE P-CLASS FIELD TOWER OF CYCLIC
EXTENSIONS OF DEGREE P. . . . 136 12.3 A CRITERION FOR INFINITE CLASS
FIELD TOWERS 144 13. THE COHOMOLOGICAL DIMENSION OF GS 149 13.1
COHOMOLOGY OF S-UNIT GROUPS 149 13.2 THE CASE S(K) = 1 154 13.3 THE CASE
S(K) =0 157 REFERENCES 163 BIBLIOGRAPHY 167 NOTATION 173 POSTSCRIPT 175
ADDITIONAL REFERENCES 181 AUTHOR INDEX 187 I SUBJECT INDEX 189
|
| any_adam_object | 1 |
| author | Koch, Helmut |
| author_facet | Koch, Helmut |
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| author_sort | Koch, Helmut |
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| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.74 |
| dewey-search | 512/.74 |
| dewey-sort | 3512 274 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T19:02:51Z |
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| isbn | 3540436294 |
| language | English German |
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| physical | XIII, 190 S. graph. Darst. |
| publishDate | 2002 |
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| spelling | Koch, Helmut Verfasser aut Galoissche Theorie der p-Erweiterungen Galois theory of p-extensions Helmut Koch Berlin [u.a.] Springer 2002 XIII, 190 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer monographs in mathematics Corpos locais larpcal Corpos p-ádicos larpcal Álgebra larpcal Algebraic fields Field extensions (Mathematics) Galois theory Group theory Algebraische Zahlentheorie (DE-588)4001170-7 gnd rswk-swf Galois-Kohomologie (DE-588)4019172-2 gnd rswk-swf Körpererweiterung (DE-588)4164435-9 gnd rswk-swf Algebraische Zahlentheorie (DE-588)4001170-7 s Körpererweiterung (DE-588)4164435-9 s Galois-Kohomologie (DE-588)4019172-2 s DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009873328&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Koch, Helmut Galois theory of p-extensions Corpos locais larpcal Corpos p-ádicos larpcal Álgebra larpcal Algebraic fields Field extensions (Mathematics) Galois theory Group theory Algebraische Zahlentheorie (DE-588)4001170-7 gnd Galois-Kohomologie (DE-588)4019172-2 gnd Körpererweiterung (DE-588)4164435-9 gnd |
| subject_GND | (DE-588)4001170-7 (DE-588)4019172-2 (DE-588)4164435-9 |
| title | Galois theory of p-extensions |
| title_alt | Galoissche Theorie der p-Erweiterungen |
| title_auth | Galois theory of p-extensions |
| title_exact_search | Galois theory of p-extensions |
| title_full | Galois theory of p-extensions Helmut Koch |
| title_fullStr | Galois theory of p-extensions Helmut Koch |
| title_full_unstemmed | Galois theory of p-extensions Helmut Koch |
| title_short | Galois theory of p-extensions |
| title_sort | galois theory of p extensions |
| topic | Corpos locais larpcal Corpos p-ádicos larpcal Álgebra larpcal Algebraic fields Field extensions (Mathematics) Galois theory Group theory Algebraische Zahlentheorie (DE-588)4001170-7 gnd Galois-Kohomologie (DE-588)4019172-2 gnd Körpererweiterung (DE-588)4164435-9 gnd |
| topic_facet | Corpos locais Corpos p-ádicos Álgebra Algebraic fields Field extensions (Mathematics) Galois theory Group theory Algebraische Zahlentheorie Galois-Kohomologie Körpererweiterung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009873328&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kochhelmut galoisschetheoriederperweiterungen AT kochhelmut galoistheoryofpextensions |