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Algebraic patching:

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Bibliographic Details
Main Author:	Yardēn, Moše 1942- (Author)
Format:	Book
Language:	English
Published:	Berlin ; Heidelberg Springer 2011
Series:	Springer monographs in mathematics
Subjects:	Proendliche Gruppe Galois-Gruppe Körperarithmetik
Online Access:	Inhaltstext Inhaltsverzeichnis
Item Description:	Literaturangaben
Physical Description:	XXII, 290 S. 24 cm
ISBN:	9783642151279

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MARC


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Record in the Search Index

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adam_text	IMAGE 1 TABLE OF CONTENTS CHAPTER 1. ALGEBRAIC PATCHING 1 1.1 PATCHING 1 1.2 GALOIS ACTION ON PATCHING DATA 5 1.3 THE COMPOUND OF THE PATCHING DATA 7 NOTES 9 CHAPTER 2. NORMED RINGS 10 2.1 NORMED RINGS 10 2.2 RINGS OF CONVERGENT POWER SERIES 14 2.3 PROPERTIES OF THE RING K{X} 17 2.4 CONVERGENT POWER SERIES 21 2.5 THE REGULARITY OF K{(X))/K({X)) 0 25 NOTES 29 CHAPTER 3. SEVERAL VARIABLES 31 3.1 A NORMED SUBRING OF K(X) 31 3.2 MITAGG-LEFFLER SERIES 33 3.3 FIELDS OF MITAGG-LEFFLER SERIES 37 3.4 FACTORIZATION OF MATRICES OVER COMPLETE RINGS 39 NOTES 41 CHAPTER 4. CONSTANT SPLIT EMBEDDING PROBLEMS OVER COMPLETE FIELDS 43 4.1 TAME REALIZATION OF CYCLIC GROUPS OVER K(X) 43 4.2 REALIZATION OF CYCLIC GROUPS OF ORDER P K 47 4.3 RATIONAL REALIZATION OF CYCLIC GROUPS OVER COMPLETE FIELDS . . 52 4.4 SOLUTION OF EMBEDDING PROBLEMS 55 NOTES 59 CHAPTER 5. AMPLE FIELDS 61 5.1 VARIETIES 61 5.2 EXISTENTIALLY CLOSED EXTENSIONS 64 5.3 AMPLE FIELDS 67 5.4 MANY POINTS 69 5.5 ALGEBRAIC EXTENSIONS 72 5.6 EXAMPLES OF AMPLE FIELDS 73 5.7 HENSELIAN PAIRS 76 5.8 FIELDS WITH PRO-P ABSOLUTE GALOIS GROUPS 81 5.9 EMBEDDING PROBLEMS OVER AMPLE FIELDS 84 5.10 PAC HILBERTIAN FIELDS ARE W-FREE 89 5.11 KRULL DOMAINS 92 5.12 LIFTING 93 NOTES 95 BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/100440980X DIGITALISIERT DURCH IMAGE 2 VIII TABLE OF CONTENTS CHAPTER 6. NON-AMPLE FIELDS 98 6.1 NONAMPLE FIELDS - ELEMENTARY METHODS 98 6.2 NONAMPLE FIELDS - ADVANCED METHODS 104 6.3 ABELIAN VARIETIES AND JACOBIAN VARIETIES 105 6.4 THE MORDELL-LANG CONJECTURE 108 6.5 CONSEQUENCES OF THE MORDELL-LANG CONJECTURE 110 6.6 ON THE GONALITY OF A FUNCTION FIELD OF ONE VARIABLE 114 6.7 GONALITY UNDER CONSTANT REDUCTION 119 6.8 POINTS OF DEGREE D 122 NOTES 127 CHAPTER 7. SPLIT EMBEDDING PROBLEMS OVER COMPLETE FIELDS 129 7.1 TOTAL DECOMPOSITION 129 7.2 RAMIFICATION 131 7.3 SOLUTION OF EMBEDDING PROBLEMS OVER COMPLETE FIELDS . . . 135 7.4 LINEARLY DISJOINT SOLUTIONS 138 NOTES 140 CHAPTER 8. SPLIT EMBEDDING PROBLEMS OVER AMPLE FIELDS 142 8.1 NORMAL REDUCTION 142 8.2 INERTIA GROUPS 145 8.3 ALMOST ALL REDUCTIONS 151 8.4 EMBEDDING PROBLEMS UNDER EXISTENTIALLY CLOSED EXTENSIONS . . 153 8.5 THE TRANSCENDENCE DEGREE OF THE FIELD OF FORMAL POWER SERIES . 157 8.6 SOLUTION OF EMBEDDING PROBLEMS OVER AMPLE FIELDS 159 NOTES 163 CHAPTER 9. THE ABSOLUTE GALOIS GROUP OF C(I) 164 9.1 THE FUNDAMENTAL GROUP OF A RIEMANN SURFACE 165 9.2 FUNDAMENTAL GROUPS IN POSITIVE CHARACTERISTIC 172 9.3 COHOMOLOGY OF GROUPS 175 9.4 THE PROJECTIVITY OF GAL(C(I)) 183 9.5 PROJECTIVITY OF FUNDAMENTAL GROUPS 186 9.6 MAXIMAL UNRAMIFIED EXTENSIONS 193 9.7 EMBEDDING PROBLEMS WITH GIVEN BRANCHING 195 9.8 DESCENT 199 9.9 FUNDAMENTAL GROUPS WITH S FINITE 202 NOTES 205 CHAPTER 10. SEMI-FREE PROFINITE GROUPS 207 10.1 INDEPENDENT SUBGROUPS 207 10.2 FIBER PRODUCTS 213 10.3 TWISTED WREATH PRODUCTS 215 10.4 CLOSED SUBGROUPS OF SEMI-FREE PROFINITE GROUPS 220 10.5 THE DIAMOND THEOREM 222 IMAGE 3 TABLE OF CONTENTS IX 10.6 QUASI-FREE PROFINITE GROUPS 227 NOTES 231 CHAPTER 11. FUNCTION FIELDS OF ONE VARIABLE OVER PAC FIELDS . . . 233 11.1 HENSELIAN FIELDS 233 11.2 BRAUER GROUPS OF HENSELIAN FIELDS 235 11.3 LOCAL-GLOBAL THEOREMS FOR BRAUER GROUPS 238 11.4 PICARD GROUPS 240 11.5 FIELDS OF COHOMOLOGICAL DIMENSION AT MOST 1 244 11.6 RADICAL EXTENSIONS 246 11.7 SEMI-FREE ABSOLUTE GALOIS GROUPS 248 NOTES 251 CHAPTER 12. COMPLETE NOETHERIAN DOMAINS 252 12.1 PERSEVERANCE OF INERTIA GROUPS 252 12.2 KRULL FIELDS 256 12.3 DENSITY OF HUBERT SETS 263 12.4 KRULL HILBERTIAN AMPLE FIELDS 268 NOTES 273 OPEN PROBLEMS 275 REFERENCES 276 GLOSSARY OF NOTATION 285 INDEX 287
any_adam_object	1
author	Yardēn, Moše 1942-
author_GND	(DE-588)122073932
author_facet	Yardēn, Moše 1942-
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dewey-ones	512 - Algebra
dewey-raw	512.3
dewey-search	512.3
dewey-sort	3512.3
dewey-tens	510 - Mathematics
discipline	Mathematik
format	Book
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indexdate	2024-08-03T01:07:18Z
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isbn	9783642151279
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physical	XXII, 290 S. 24 cm
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spelling	Yardēn, Moše 1942- Verfasser (DE-588)122073932 aut Algebraic patching Moshe Jarden Berlin ; Heidelberg Springer 2011 XXII, 290 S. 24 cm txt rdacontent n rdamedia nc rdacarrier Springer monographs in mathematics Literaturangaben Proendliche Gruppe (DE-588)4132444-4 gnd rswk-swf Galois-Gruppe (DE-588)4155897-2 gnd rswk-swf Körperarithmetik (DE-588)7735089-3 gnd rswk-swf Körperarithmetik (DE-588)7735089-3 s Galois-Gruppe (DE-588)4155897-2 s Proendliche Gruppe (DE-588)4132444-4 s DE-604 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3513925&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026909885&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Yardēn, Moše 1942- Algebraic patching Proendliche Gruppe (DE-588)4132444-4 gnd Galois-Gruppe (DE-588)4155897-2 gnd Körperarithmetik (DE-588)7735089-3 gnd
subject_GND	(DE-588)4132444-4 (DE-588)4155897-2 (DE-588)7735089-3
title	Algebraic patching
title_auth	Algebraic patching
title_exact_search	Algebraic patching
title_full	Algebraic patching Moshe Jarden
title_fullStr	Algebraic patching Moshe Jarden
title_full_unstemmed	Algebraic patching Moshe Jarden
title_short	Algebraic patching
title_sort	algebraic patching
topic	Proendliche Gruppe (DE-588)4132444-4 gnd Galois-Gruppe (DE-588)4155897-2 gnd Körperarithmetik (DE-588)7735089-3 gnd
topic_facet	Proendliche Gruppe Galois-Gruppe Körperarithmetik
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work_keys_str_mv	AT yardenmose algebraicpatching

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