Local class field theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Oxford Univ. Press
1986
Oxford Clarendon Press |
| Schriftenreihe: | Oxford mathematical monographs
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus d. Japan. übers. |
| Beschreibung: | VIII, 155 S. |
| ISBN: | 0195040309 |
Internformat
MARC
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| 245 | 1 | 0 | |a Local class field theory |c Kenkichi Iwasawa |
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Datensatz im Suchindex
| _version_ | 1804114979093217280 |
|---|---|
| adam_text | Contents
Chapter I. Valuations 3
1.1. Some Basic Definitions 3
1.2. Complete Fields 7
1.3. Finite Extensions of Complete Fields 12
Chapter II. Local Fields 18
2.1. General Properties 18
2.2. The Multiplicative Group k* 22
2.3. Finite Extensions 25
2.4. The Different and the Discriminant 29
2.5. Finite Galois Extensions 32
Chapter III. Infinite Extensions of Local Fields 35
3.1. Algebraic Extensions and Their Completions 35
3.2. Unramified Extensions and Totally Ramified Extensions 36
3.3. The Norm Groups 40
3.4. Formal Power Series 43
3.5. Power Series over o^ 45
Chapter IV. Formal Groups Ff(X, Y) 50
4.1. Formal Groups in General 50
4.2. Formal Groups Ff(X, Y) 53
4.3. The o Modules Wnf 57
4.4. Extensions L /K 61
Chapter V. Abelian Extensions Defined by Formal Groups 65
5.1. Abelian Extensions L and kâ„¢n 65
5.2. The Norm Operator of Coleman 69
5.3. Abelian Extensions L and kK 75
Chapter VI. Fundamental Theorems 80
6.1. The Homomorphism pk 80
6.2. Proof of Lk = kab 84
6.3. The Norm Residue Map 88
viii Contents
Chapter VII. Finite Abelian Extensions 98
7.1. Norm Groups of Finite Abelian Extensions 98
7.2. Ramification Groups in the Upper Numbering 101
7.3. The Special Case k% /k 107
7.4. Some Applications 110
Chapter VIII. Explicit Formulas 116
8.1. ^ Sequences 116
8.2. The Pairing (a , fi)f 120
8.3. The Pairing [a, ]„ 123
8.4. The Main Theorem 127
8.5. The Special Case for k = Qp 133
Appendix 137
A.I. Galois Cohomology Groups 137
A.2. The Brauer Group of a Local Field 141
A.3. The Method of Hazewinkel 146
Bibliography 151
Table of Notations 153
Index 155
|
| any_adam_object | 1 |
| author | Iwasawa, Kenkichi 1917-1998 |
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| author_facet | Iwasawa, Kenkichi 1917-1998 |
| author_role | aut |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 180 SK 230 |
| classification_tum | MAT 123f |
| ctrlnum | (OCoLC)12944732 (DE-599)BVBBV000531763 |
| dewey-full | 512/.74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| 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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| id | DE-604.BV000531763 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:15:19Z |
| institution | BVB |
| isbn | 0195040309 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000328071 |
| oclc_num | 12944732 |
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| owner_facet | DE-12 DE-91G DE-BY-TUM DE-384 DE-703 DE-739 DE-355 DE-BY-UBR DE-29T DE-19 DE-BY-UBM DE-706 DE-83 DE-11 |
| physical | VIII, 155 S. |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | Oxford Univ. Press Clarendon Press |
| record_format | marc |
| series2 | Oxford mathematical monographs |
| spelling | Iwasawa, Kenkichi 1917-1998 Verfasser (DE-588)118961373 aut Kyokusho ruitai ron Local class field theory Kenkichi Iwasawa New York Oxford Univ. Press 1986 Oxford Clarendon Press VIII, 155 S. txt rdacontent n rdamedia nc rdacarrier Oxford mathematical monographs Aus d. Japan. übers. Class field theory Lokale Klassenkörpertheorie (DE-588)4168107-1 gnd rswk-swf Lokale Klassenkörpertheorie (DE-588)4168107-1 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000328071&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Iwasawa, Kenkichi 1917-1998 Local class field theory Class field theory Lokale Klassenkörpertheorie (DE-588)4168107-1 gnd |
| subject_GND | (DE-588)4168107-1 |
| title | Local class field theory |
| title_alt | Kyokusho ruitai ron |
| title_auth | Local class field theory |
| title_exact_search | Local class field theory |
| title_full | Local class field theory Kenkichi Iwasawa |
| title_fullStr | Local class field theory Kenkichi Iwasawa |
| title_full_unstemmed | Local class field theory Kenkichi Iwasawa |
| title_short | Local class field theory |
| title_sort | local class field theory |
| topic | Class field theory Lokale Klassenkörpertheorie (DE-588)4168107-1 gnd |
| topic_facet | Class field theory Lokale Klassenkörpertheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000328071&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT iwasawakenkichi kyokushoruitairon AT iwasawakenkichi localclassfieldtheory |