Arithmetic differential equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2005]
|
| Series: | Mathematical surveys and monographs
volume 118 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xxxii, 310 Seiten |
| ISBN: | 0821838628 9780821838624 |
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Record in the Search Index
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| adam_text | MATHEMATICAL SURVEYS AND MONOGRAPHS VOLUME 118 ARITHMETIC DIFFERENTIAL
EQUATIONS ALEXANDRU BUIUM AMERICAN MATHEMATICAL SOCIETY CONTENTS PREFACE
VII INTRODUCTION XI 0.1. MOTIVATION AND STRATEGY XI 0.2. ROUGH OUTLINE
OF THE THEORY XIV 0.3. COMPARISON WITH OTHER THEORIES XIX PART 1. MAIN
CONCEPTS AND RESULTS 1 CHAPTER 1. PRELIMINARIES FROM ALGEBRAIC GEOMETRY
3 1.1. ALGEBRO-GEOMETRIC TERMINOLOGY 3 1.2. CATEGORICAL QUOTIENTS IN
ALGEBRAIC GEOMETRY 11 1.3. ANALYTIC UNIFORMIZATION AND CRITICAL
FINITENESS 15 CHAPTER 2. OUTLINE OF 5* GEOMETRY . 31 2.1. MAIN CONCEPTS
OF 5 -GEOMETRY 31 2.2. MAIN CONJECTURES 55 2.3. MAIN RESULTS: A SAMPLE
56 2.4. APPENDIX: AXIOMATIC CHARACTERIZATION OF 5* GEOMETRIES 61 PART 2.
GENERAL THEORY 69 CHAPTER 3. GLOBAL THEORY 71 3.1. P* JET SPACES OF
SCHEMES 71 3.2. BEHAVIOR WITH RESPECT TO ETALE MAPS 75 3.3. LINK BETWEEN
P* JET SPACES AND 5* FUNCTIONS 78 3.4. GALOIS COVERS 82 3.5. 6* BASE
LOCI VERSUS POSTCRITICAL LOCI 85 3.6. 6* TANGENT MAPS AND 6*
DIFFERENTIALS OF S* FUNCTIONS 88 CHAPTER 4. LOCAL THEORY 107 4.1. LOCAL
ANALOGUE OF THE MAIN CONJECTURES 107 4.2. BOUNDING THE RANK OF THE
MODULE OF S* INVARIANTS 119 4.3. 5* INVARIANTS FOR THE FORMAL
MULTIPLICATIVE GROUP 121 4.4. P* JETS OF FORMAL GROUP LAWS 123 4.5.
LOCAL VERSUS GLOBAL PICTURE: FIXED POINTS AND CYCLES 126 4.6. SOME
GENERAL GLOBAL CONVERSE RESULTS 132 CHAPTER 5. BIRATIONAL THEORY 141
5.1. THE BASIC GRADED RINGS 141 5.2. (^-GALOIS GROUPS 145 VI CONTENTS
5.3. 6* INVARIANTS FOR SUBGROUPS OF PGL 2 (Z P ) 147 PART 3.
APPLICATIONS 159 CHAPTER 6. SPHERICAL CORRESPONDENCES 161 6.1. SPHERICAL
CORRESPONDENCES OVER R AND THEIR CYCLES 161 6.2. 5*SECTIONS OF BUNDLES
ON THE PROJECTIVE LINE 165 6.3. CASE F TRIVIAL: ^-INVARIANTS AND
6-COHOMOLOGY 167 6.4. CASE F NON-TRIVIAL: S* INVARIANTS, 5* COHOMOLOGY
AND 5* FIBER 173 6.5. CASE (R, R) SOLVABLE 178 6.6. A CONVERSE THEOREM:
BIQUADRATIC CORRESPONDENCES 181 CHAPTER 7. FLAT CORRESPONDENCES 185 7.1.
FLAT CORRESPONDENCES OVER R: S* LINE BUNDLES AND CYCLES 185 7.2.
(5-CHARACTERS 190 7.3. (5-INVARIANTS 205 7.4. S-BASE LOCI 210 7.5. 5*
COHOMOLOGY 212 7.6. THE RELATIVE GENERIC 6-FIBER 221 7.7. CONVERSE
THEOREMS: QUADRATIC DYNAMICAL SYSTEMS 223 CHAPTER 8. HYPERBOLIC
CORRESPONDENCES 227 8.1. REVIEW OF ABELIAN SCHEMES AND THEIR CRYSTALS
228 8.2. HECKE CORRESPONDENCES OVER R: 5* LINE BUNDLES AND CYCLES 240
8.3. 6* SERRE-TATE EXPANSION MAPS AND S* SERRE OPERATORS 251 8.4.
CONSTRUCTIONS OF 5* INVARIANTS 260 8.5. 5* INVARIANTS IN THE ORDINARY
CASE 275 8.6. 8* INVARIANTS IN THE NON-ORDINARY CASE 279 8.7. 5*
COHOMOLOGY 285 8.8. THE RELATIVE GENERIC 5-FIBER 288 8.9. HECKE
CORRESPONDENCES WITH A REGULAR HECKE N* CYCLE 292 8.10. A CONVERSE
THEOREM: NON-RATIONAL HYPERBOLIC UNIFORMIZATION 295 LIST OF RESULTS 299
BIBLIOGRAPHY 301 INDEX 307
|
| adam_txt |
MATHEMATICAL SURVEYS AND MONOGRAPHS VOLUME 118 ARITHMETIC DIFFERENTIAL
EQUATIONS ALEXANDRU BUIUM AMERICAN MATHEMATICAL SOCIETY CONTENTS PREFACE
VII INTRODUCTION XI 0.1. MOTIVATION AND STRATEGY XI 0.2. ROUGH OUTLINE
OF THE THEORY XIV 0.3. COMPARISON WITH OTHER THEORIES XIX PART 1. MAIN
CONCEPTS AND RESULTS 1 CHAPTER 1. PRELIMINARIES FROM ALGEBRAIC GEOMETRY
3 1.1. ALGEBRO-GEOMETRIC TERMINOLOGY 3 1.2. CATEGORICAL QUOTIENTS IN
ALGEBRAIC GEOMETRY 11 1.3. ANALYTIC UNIFORMIZATION AND CRITICAL
FINITENESS 15 CHAPTER 2. OUTLINE OF 5* GEOMETRY . 31 2.1. MAIN CONCEPTS
OF 5 -GEOMETRY 31 2.2. MAIN CONJECTURES 55 2.3. MAIN RESULTS: A SAMPLE
56 2.4. APPENDIX: AXIOMATIC CHARACTERIZATION OF 5* GEOMETRIES 61 PART 2.
GENERAL THEORY 69 CHAPTER 3. GLOBAL THEORY 71 3.1. P* JET SPACES OF
SCHEMES 71 3.2. BEHAVIOR WITH RESPECT TO ETALE MAPS 75 3.3. LINK BETWEEN
P* JET SPACES AND 5* FUNCTIONS 78 3.4. GALOIS COVERS 82 3.5. 6* BASE
LOCI VERSUS POSTCRITICAL LOCI 85 3.6. 6* TANGENT MAPS AND 6*
DIFFERENTIALS OF S* FUNCTIONS 88 CHAPTER 4. LOCAL THEORY 107 4.1. LOCAL
ANALOGUE OF THE MAIN CONJECTURES 107 4.2. BOUNDING THE RANK OF THE
MODULE OF S* INVARIANTS 119 4.3. 5* INVARIANTS FOR THE FORMAL
MULTIPLICATIVE GROUP 121 4.4. P* JETS OF FORMAL GROUP LAWS 123 4.5.
LOCAL VERSUS GLOBAL PICTURE: FIXED POINTS AND CYCLES 126 4.6. SOME
GENERAL GLOBAL CONVERSE RESULTS 132 CHAPTER 5. BIRATIONAL THEORY 141
5.1. THE BASIC GRADED RINGS 141 5.2. (^-GALOIS GROUPS 145 VI CONTENTS
5.3. 6* INVARIANTS FOR SUBGROUPS OF PGL 2 (Z P ) 147 PART 3.
APPLICATIONS 159 CHAPTER 6. SPHERICAL CORRESPONDENCES 161 6.1. SPHERICAL
CORRESPONDENCES OVER R AND THEIR CYCLES 161 6.2. 5*SECTIONS OF BUNDLES
ON THE PROJECTIVE LINE 165 6.3. CASE F TRIVIAL: ^-INVARIANTS AND
6-COHOMOLOGY 167 6.4. CASE F NON-TRIVIAL: S* INVARIANTS, 5* COHOMOLOGY
AND 5* FIBER 173 6.5. CASE (R, R) SOLVABLE 178 6.6. A CONVERSE THEOREM:
BIQUADRATIC CORRESPONDENCES 181 CHAPTER 7. FLAT CORRESPONDENCES 185 7.1.
FLAT CORRESPONDENCES OVER R: S* LINE BUNDLES AND CYCLES 185 7.2.
(5-CHARACTERS 190 7.3. (5-INVARIANTS 205 7.4. S-BASE LOCI 210 7.5. 5*
COHOMOLOGY 212 7.6. THE RELATIVE GENERIC 6-FIBER 221 7.7. CONVERSE
THEOREMS: QUADRATIC DYNAMICAL SYSTEMS 223 CHAPTER 8. HYPERBOLIC
CORRESPONDENCES 227 8.1. REVIEW OF ABELIAN SCHEMES AND THEIR CRYSTALS
228 8.2. HECKE CORRESPONDENCES OVER R: 5* LINE BUNDLES AND CYCLES 240
8.3. 6* SERRE-TATE EXPANSION MAPS AND S* SERRE OPERATORS 251 8.4.
CONSTRUCTIONS OF 5* INVARIANTS 260 8.5. 5* INVARIANTS IN THE ORDINARY
CASE 275 8.6. 8* INVARIANTS IN THE NON-ORDINARY CASE 279 8.7. 5*
COHOMOLOGY 285 8.8. THE RELATIVE GENERIC 5-FIBER 288 8.9. HECKE
CORRESPONDENCES WITH A REGULAR HECKE N* CYCLE 292 8.10. A CONVERSE
THEOREM: NON-RATIONAL HYPERBOLIC UNIFORMIZATION 295 LIST OF RESULTS 299
BIBLIOGRAPHY 301 INDEX 307 |
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| index_date | 2024-07-02T13:16:38Z |
| indexdate | 2024-07-09T20:26:22Z |
| institution | BVB |
| isbn | 0821838628 9780821838624 |
| language | English |
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| physical | xxxii, 310 Seiten |
| publishDate | 2005 |
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| spelling | Buium, Alexandru 1955- Verfasser (DE-588)111183804 aut Arithmetic differential equations Alexandru Buium Providence, Rhode Island American Mathematical Society [2005] © 2005 xxxii, 310 Seiten txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs volume 118 Geometria algébrica larpcal Geometria aritmética larpcal Géométrie algébrique arithmétique Géométrie algébrique arithmétique rasuqam Riemann, Surfaces de Surface de Riemann rasuqam Équation différentielle rasuqam Arithmetical algebraic geometry Riemann surfaces Arithmetische Geometrie (DE-588)4131383-5 gnd rswk-swf Riemannsche Fläche (DE-588)4049991-1 gnd rswk-swf Arithmetische Geometrie (DE-588)4131383-5 s Riemannsche Fläche (DE-588)4049991-1 s b DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1345-3 Mathematical surveys and monographs volume 118 (DE-604)BV000018014 118 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014163172&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Buium, Alexandru 1955- Arithmetic differential equations Mathematical surveys and monographs Geometria algébrica larpcal Geometria aritmética larpcal Géométrie algébrique arithmétique Géométrie algébrique arithmétique rasuqam Riemann, Surfaces de Surface de Riemann rasuqam Équation différentielle rasuqam Arithmetical algebraic geometry Riemann surfaces Arithmetische Geometrie (DE-588)4131383-5 gnd Riemannsche Fläche (DE-588)4049991-1 gnd |
| subject_GND | (DE-588)4131383-5 (DE-588)4049991-1 |
| title | Arithmetic differential equations |
| title_auth | Arithmetic differential equations |
| title_exact_search | Arithmetic differential equations |
| title_exact_search_txtP | Arithmetic differential equations |
| title_full | Arithmetic differential equations Alexandru Buium |
| title_fullStr | Arithmetic differential equations Alexandru Buium |
| title_full_unstemmed | Arithmetic differential equations Alexandru Buium |
| title_short | Arithmetic differential equations |
| title_sort | arithmetic differential equations |
| topic | Geometria algébrica larpcal Geometria aritmética larpcal Géométrie algébrique arithmétique Géométrie algébrique arithmétique rasuqam Riemann, Surfaces de Surface de Riemann rasuqam Équation différentielle rasuqam Arithmetical algebraic geometry Riemann surfaces Arithmetische Geometrie (DE-588)4131383-5 gnd Riemannsche Fläche (DE-588)4049991-1 gnd |
| topic_facet | Geometria algébrica Geometria aritmética Géométrie algébrique arithmétique Riemann, Surfaces de Surface de Riemann Équation différentielle Arithmetical algebraic geometry Riemann surfaces Arithmetische Geometrie Riemannsche Fläche |
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