Verfügbarkeit: Local fields :: THWS Bibkatalog

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Bibliographische Detailangaben
1. Verfasser:	Serre, Jean-Pierre 1926- (VerfasserIn)
Format:	Buch
Sprache:	German English French
Veröffentlicht:	New York [u.a.] Springer 1995
Ausgabe:	(2., corr. printing)
Schriftenreihe:	Graduate texts in mathematics 67
Schlagworte:	Teoria analítica dos números Teoria dos números Teoria geométrica dos números Teoria homológica Homology theory Local fields (Algebra) Klassenkörpertheorie Kohomologie Homologietheorie Lokale Klassenkörpertheorie Körpertheorie Lokaler Körper Kommutative Algebra Lokale Klasse
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	Literaturverz. S. 232 - 237. - Hier auch später erschienene, unveränderte Nachdrucke
Beschreibung:	VIII, 241 S.
ISBN:	0387904247 3540904247 9780387904245

Internformat

MARC


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Datensatz im Suchindex

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adam_text	JEAN-PIERRE SERRE LOCAL FIELDS TRANSLATED FROM THE FRENCH BY MARVIN JAY GREENBERG SPRINGER CONTENTS INTRODUCTION 1 LEITFADEN 2 PART ONE * LOCAL FIELDS (BASIC FACTS) CHAPTER I , , DISCRETE VALUATION RINGS AND DEDEKIND DOMAINS 5 §1. DEFINITION OF DISCRETE VALUATION RING 5 §2. CHARACTERISATIONS OF DISCRETE VALUATION RINGS 7 §3. DEDEKIND DOMAINS 9 §4. EXTENSIONS . 13 §5. THE NORM AND INCLUSION HOMOMORPHISMS 15 §6. EXAMPLE: SIMPLE EXTENSIONS 17 §7. GALOIS EXTENSIONS 20 §8. FROBENIUS SUBSTITUTION 23 CHAPTER II COMPLETION 26 §1. ABSOLUTE VALUES AND THE TOPOLOGY DEFINED BY A DISCRETE VALUATION 26 §2. EXTENSIONS OF A COMPLETE FIELD 28 §3. EXTENSION AND COMPLETION 30 §4. STRUCTURE OF COMPLETE DISCRETE VALUATION RINGS I: EQUAL CHARACTERISTIC CASE 32 §5. STRUCTURE OF COMPLETE DISCRETE VALUATION RINGS II: UNEQUAL CHARACTERISTIC CASE 36 §6. WITT VECTORS 40 VI CONTENTS PART TWO RAMIFICATION CHAPTER HI DISCRIMINANT AND DIFFERENT 47 §1. LATTICES 47 §2. DISCRIMINANT OF A LATTICE WITH RESPECT TO A BILINEAR FORM 48 §3. DISCRIMINANT AND DIFFERENT OF A SEPARABLE EXTENSION 50 §4. ELEMENTARY PROPERTIES OF THE DIFFERENT AND DISCRIMINANT 51 §5. UNRAMIFIED EXTENSIONS 53 §6. COMPUTATION OF DIFFERENT AND DISCRIMINANT 55 §7. A DIFFERENTIAL CHARACTERISATION OF THE DIFFERENT 59 CHAPTER IV RAMIFICATION GROUPS 61 §1. DEFINITION OF THE RAMIFICATION GROUPS; FIRST PROPERTIES 61 §2. THE QUOTIENTS G,/G 1+ * I 0 65 §3. THE FUNCTIONS / AND I/F; HERBRAND S THEOREM 73 §4. EXAMPLE: CYCLOTOMIC EXTENSIONS OF THE FIELD Q P 77 CHAPTER V THE NORM 80 §1. LEMMAS 80 §2. THE UNRAMIFIED CASE 81 §3. THE CYCLIC OF PRIME ORDER TOTALLY RAMIFIED CASE 83 §4. EXTENSION OF THE RESIDUE FIELD IN A TOTALLY RAMIFIED EXTENSION 87 §5. MULTIPLICATIVE POLYNOMIALS AND ADDITIVE POLYNOMIALS 90 §6. THE GALOIS TOTALLY RAMIFIED CASE 91 §7. APPLICATION: PROOF OF THE HASSE-ARF THEOREM 93 CHAPTER VI ARTIN REPRESENTATION 97 §1. REPRESENTATIONS AND CHARACTERS 97 §2. ARTIN REPRESENTATION 99 §3. GLOBALISATION 103 §4. ARTIN REPRESENTATION AND HOMOLOGY (FOR ALGEBRAIC CURVES) 105 PART THREE GROUP COHOMOLOGY CHAPTER VII 109 BASIC FACTS §1. G-MODULES 109 §2. COHOMOLOGY 111 §3. COMPUTING THE COHOMOLOGY VIA COCHAINS 112 CONTENTS VLI §4. HOMOLOGY 114 §5. CHANGE OF GROUP 115 §6. AN EXACT SEQUENCE 117 §7. SUBGROUPS OF FINITE INDEX 118 §8. TRANSFER 120 APPENDIX NON-ABELIAN COHOMOLOGY 123 CHAPTER VIII COHOMOLOGY OF FINITE GROUPS 127 §1. THE TATE COHOMOLOGY GROUPS 127 §2. RESTRICTION AND CORESTRICTION 129 §3. CUP PRODUCTS 131 §4. COHOMOLOGY OF FINITE CYCLIC GROUPS. HERBRAND QUOTIENT 132 §5. HERBRAND QUOTIENT IN THE CYCLIC OF PRIME ORDER CASE 134 CHAPTER IX THEOREMS OF TATE AND NAKAYAMA 138 §1. P-GROUPS 138 §2. SYLOW SUBGROUPS 139 §3. INDUCED MODULES; COHOMOLOGICALLY TRIVIAL MODULES 141 §4. COHOMOLOGY OF A P-GROUP 142 §5. COHOMOLOGY OF A FINITE GROUP 144 §6. DUAL RESULTS 146 §7. COMPARISON THEOREM 147 §8. THE THEOREM OF TATE AND NAKAYAMA- 148 CHAPTER X GALOIS COHOMOLOGY O 150 §1. FIRST EXAMPLES 150 §2. SEVERAL EXAMPLES OF DESCENT 152 §3. INFINITE GALOIS EXTENSIONS 154 §4. THE BRAUER GROUP 155 §5. COMPARISON WITH THE CLASSICAL DEFINITION OF THE BRAUER GROUP . 157 §6. GEOMETRIC INTERPRETATION OF THE BRAUER GROUP: SEVERI-BRAUER VARIETIES 160 §7. EXAMPLES OF BRAUER GROUPS 161 CHAPTER XI ^ CLASS FORMATIONS 164 §1. THE NOTION OF FORMATION 164 §2. CLASS FORMATIONS 166 §3. FUNDAMENTAL CLASSES AND RECIPROCITY ISOMORPHISM 168 §4. ABELIAN EXTENSIONS AND NORM GROUPS 171 §5. THE EXISTENCE THEOREM 173 APPENDIX COMPUTATIONS OF CUP PRODUCTS 176 VLLL CONTENTS PART FOUR LOCAL CLASS FIELD THEORY CHAPTER XII BRAUER GROUP OF A LOCAL FIELD 181 § 1. EXISTENCE OF AN UNRAMIFIED SPLITTING FIELD 181 §2. EXISTENCE OF AN UNRAMIFIED SPLITTING FIELD (DIRECT PROOF) 182 §3. DETERMINATION OF THE BRAUER GROUP 184 CHAPTER XIII LOCAL CLASS FIELD THEORY 188 §1. THE GROUP Z AND ITS COHOMOLOGY 188 §2. QUASI-FINITE FIELDS 190 §3. THE BRAUER GROUP 192 §4. CLASS FORMATION 195 §5. DWORK S THEOREM 199 CHAPTER XIV LOCAL SYMBOLS AND EXISTENCE THEOREM 204 §1. GENERAL DEFINITION OF LOCAL SYMBOLS 204 §2. THE SYMBOL (A, B) 205 §3. COMPUTATION OF THE SYMBOL {A, B) V IN THE TAMELY RAMIFIED CASE 209 §4. COMPUTATION OF THE SYMBOL (A, B) V FOR THE FIELD Q P (N = 2) 211 §5. THE SYMBOLS [A, B) 214 §6. THE EXISTENCE THEOREM 218 §7. EXAMPLE: THE MAXIMAL ABELIAN EXTENSION OF Q P 220 APPENDIX THE GLOBAL CASE (STATEMENT OF RESULTS) 221 CHAPTER XV RAMIFICATION 223 §1. KERNEL AND COKERNEL OF AN ADDITIVE (RESP. MULTIPLICATIVE) POLYNOMIAL 223 §2. THE NORM GROUPS 226 §3. EXPLICIT COMPUTATIONS 229 BIBLIOGRAPHY 232 SUPPLEMENTARY BIBLIOGRAPHY FOR THE ENGLISH EDITIORF 235 INDEX 239
any_adam_object	1
author	Serre, Jean-Pierre 1926-
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edition	(2., corr. printing)
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id	DE-604.BV010669832
illustrated	Not Illustrated
indexdate	2024-07-09T17:56:58Z
institution	BVB
isbn	0387904247 3540904247 9780387904245
language	German English French
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-007122392
oclc_num	33164798
open_access_boolean
owner	DE-12 DE-355 DE-BY-UBR DE-11 DE-19 DE-BY-UBM
owner_facet	DE-12 DE-355 DE-BY-UBR DE-11 DE-19 DE-BY-UBM
physical	VIII, 241 S.
publishDate	1995
publishDateSearch	1995
publishDateSort	1995
publisher	Springer
record_format	marc
series	Graduate texts in mathematics
series2	Graduate texts in mathematics
spelling	Serre, Jean-Pierre 1926- Verfasser (DE-588)142283126 aut Corps locaux Local fields Jean-Pierre Serre (2., corr. printing) New York [u.a.] Springer 1995 VIII, 241 S. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 67 Literaturverz. S. 232 - 237. - Hier auch später erschienene, unveränderte Nachdrucke Teoria analítica dos números larpcal Teoria dos números larpcal Teoria geométrica dos números larpcal Teoria homológica larpcal Homology theory Local fields (Algebra) Klassenkörpertheorie (DE-588)4030951-4 gnd rswk-swf Kohomologie (DE-588)4031700-6 gnd rswk-swf Homologietheorie (DE-588)4141714-8 gnd rswk-swf Lokale Klassenkörpertheorie (DE-588)4168107-1 gnd rswk-swf Körpertheorie (DE-588)4164455-4 gnd rswk-swf Lokaler Körper (DE-588)4266744-6 gnd rswk-swf Kommutative Algebra (DE-588)4164821-3 gnd rswk-swf Lokale Klasse (DE-588)4577640-4 gnd rswk-swf Lokale Klassenkörpertheorie (DE-588)4168107-1 s Kohomologie (DE-588)4031700-6 s DE-604 Körpertheorie (DE-588)4164455-4 s Lokale Klasse (DE-588)4577640-4 s 1\p DE-604 Lokaler Körper (DE-588)4266744-6 s 2\p DE-604 Kommutative Algebra (DE-588)4164821-3 s 3\p DE-604 Homologietheorie (DE-588)4141714-8 s 4\p DE-604 Klassenkörpertheorie (DE-588)4030951-4 s 5\p DE-604 Erscheint auch als Online-Ausgabe 978-1-4757-5673-9 Graduate texts in mathematics 67 (DE-604)BV000000067 67 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007122392&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Serre, Jean-Pierre 1926- Local fields Graduate texts in mathematics Teoria analítica dos números larpcal Teoria dos números larpcal Teoria geométrica dos números larpcal Teoria homológica larpcal Homology theory Local fields (Algebra) Klassenkörpertheorie (DE-588)4030951-4 gnd Kohomologie (DE-588)4031700-6 gnd Homologietheorie (DE-588)4141714-8 gnd Lokale Klassenkörpertheorie (DE-588)4168107-1 gnd Körpertheorie (DE-588)4164455-4 gnd Lokaler Körper (DE-588)4266744-6 gnd Kommutative Algebra (DE-588)4164821-3 gnd Lokale Klasse (DE-588)4577640-4 gnd
subject_GND	(DE-588)4030951-4 (DE-588)4031700-6 (DE-588)4141714-8 (DE-588)4168107-1 (DE-588)4164455-4 (DE-588)4266744-6 (DE-588)4164821-3 (DE-588)4577640-4
title	Local fields
title_alt	Corps locaux
title_auth	Local fields
title_exact_search	Local fields
title_full	Local fields Jean-Pierre Serre
title_fullStr	Local fields Jean-Pierre Serre
title_full_unstemmed	Local fields Jean-Pierre Serre
title_short	Local fields
title_sort	local fields
topic	Teoria analítica dos números larpcal Teoria dos números larpcal Teoria geométrica dos números larpcal Teoria homológica larpcal Homology theory Local fields (Algebra) Klassenkörpertheorie (DE-588)4030951-4 gnd Kohomologie (DE-588)4031700-6 gnd Homologietheorie (DE-588)4141714-8 gnd Lokale Klassenkörpertheorie (DE-588)4168107-1 gnd Körpertheorie (DE-588)4164455-4 gnd Lokaler Körper (DE-588)4266744-6 gnd Kommutative Algebra (DE-588)4164821-3 gnd Lokale Klasse (DE-588)4577640-4 gnd
topic_facet	Teoria analítica dos números Teoria dos números Teoria geométrica dos números Teoria homológica Homology theory Local fields (Algebra) Klassenkörpertheorie Kohomologie Homologietheorie Lokale Klassenkörpertheorie Körpertheorie Lokaler Körper Kommutative Algebra Lokale Klasse
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007122392&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000000067
work_keys_str_mv	AT serrejeanpierre corpslocaux AT serrejeanpierre localfields

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