The ball and some Hilbert problems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
1995
|
| Series: | Lectures in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VI, 160 S. graph. Darst. |
| ISBN: | 3764328355 0817628355 |
Staff View
MARC
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Record in the Search Index
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| adam_text | IMAGE 1
ROLF-PETER HOLZAPFEL
THE BALL AND SOME HILBERT PROBLEMS
1995 BIRKHAUSER VERLAG
BASEL * BOSTON * BERLIN
IMAGE 2
CONTENTS
PREFACE VII
1 ELLIPTIC CURVES, THE FINITENESS THEOREM OF SHAFAREVIC 1
1.1 ELLIPTIC CURVES OVER C 1
1.2 ELLIPTIC CURVES OVER ARBITRARY FIELDS 4
1.2.1 REDUCTION OF ELLIPTIC CURVES 6
1.2.2 TWO FINITENESS THEOREMS OF NUMBER THEORY 6
1.2.3 SHAFAREVIC S FINITENESS THEOREM 7
1.2.4 BASIC REFERENCES 9
2 PICARD CURVES 11
2.1 THE MODULI SPACE OF PICARD CURVES 11
2.2 THE RELATIVE SCHOTTKY PROBLEM FOR PICARD CURVES 17
2.2.1 THE JACOBI MAP 19
2.2.2 RIEMANN S PERIOD RELATIONS 19
2.2.3 THE EFFECTIVE SCHOTTKY-TORELLI PROBLEM FOR PICARD CURVES 21
2.3 TYPICAL PERIOD MATRICES 22
2.3.1 G-TYPICAL BASES OF #I(Z) 23
2.3.2 PERIOD MATRICES OF G-TYPICAL BASES 25
2.4 METRIZATION 26
2.5 ARITHMETIZATION 29
2.6 A RETROSPECT TO ELLIPTIC CURVES 31
2.7 ROUGH SOLUTION OF THE RELATIVE SCHOTTKY PROBLEM FOR PICARD CURVES 33
3 UNIFORMIZATIONS AND DIFFERENTIAL EQUATIONS OF EULER-PICARD TYPE 39
3.1 BALL UNIFORMIZATION OF ALGEBRAIC SURFACES 39
3.2 SPECIAL FUCHSIAN SYSTEMS AND GAUSS-MANIN CONNECTION 45
3.3 PICARD MODULAR FORMS 52
3.4 PICARD MODULAR FORMS AS THETA CONSTANTS 59
4 ALGEBRAIC VALUES OF PICARD MODULAR THETA FUNCTIONS 65
4.1 INTRODUCTION 65
4.2 COMPLEX MULTIPLICATION ON ABELIAN VARIETIES 67
4.3 TYPES OF COMPLEX MULTIPLICATION 69
4.4 TRANSFORMATION OF CONSTANTS 75
4.5 SHIMURA CLASS FIELDS 77
4.6 MODULI FIELDS 79
4.7 THE MAIN THEOREM OF COMPLEX MULTIPLICATION 81
4.8 SHIMURA CLASS FIELDS BY SPECIAL VALUES 83
4.9 SPECIAL POINTS ON SHIMURA VARIETIES OF U(2,1) 87
IMAGE 3
VI CONTENTS
5 TRANSCENDENTAL VALUES OF PICARD MODULAR THETA CONSTANTS 101 5.1
TRANSCENDENCE AT NON-SINGULAR SIMPLE ALGEBRAIC MODULI 101
5.2 TRANSCENDENCE AT NON-SINGULAR NON-SIMPLE ALGEBRAIC MODULI 109 5.3
SOME MORE HISTORY 114
6 ARITHMETIC SURFACES OF KODAIRA-PICARD TYPE AND SOME DIOPHANTINE
EQUATIONS 119
6.1 INTRODUCTION 119
6.2 ARITHMETIC SURFACES AND CURVES OF KODAIRA-PICARD TYPE 119
6.3 HEIGHTS 120
6.4 CONJECTURES OF V O J TA AND PARSHIN S PROBLEM 125
6.5 KUMMER MAPS 127
6.6 PROOF OF THE MAIN IMPLICATION 128
7 APPENDIX I A FINITENESS THEOREM FOR PICARD CURVES WITH GOOD REDUCTION
133
7.1 SOME DEFINITIONS AND KNOWN RESULTS 133
7.2 AFFINE MODELS OF N-GONAL CYCLIC CURVES 134
7.3 NORMAL FORMS OF PICARD CURVES 135
7.4 CONDITIONS FOR SMOOTHNESS 138
7.5 PROJECTIVE ISOMORPHISM CLASSIFICATION IN CHARACTERISTIC 3 139
7.6 MINIMAL NORMAL FORMS FOR PLCARD CURVES 140
7.7 GOOD REDUCTION OF PICARD CURVES 141
8 APPENDIX II THE HILBERT PROBLEMS 7, 12, 21 AND 22 145
8.1 IRRATIONALITY AND TRANSCENDENCE OF CERTAIN NUMBERS 145
8.2 EXTENSION OF KRONECKER S THEOREM ON ABELIAN FIELDS 145
8.3 PROOF OF THE EXISTENCE OF LINEAR DIFFERENTIAL EQUATIONS HAVING A
PRESCRIBED MONODROMIC GROUP 147
8.4 UNIFORMIZATION OF ANALYTIC RELATIONS BY MEANS OF AUTOMORPHIC
FUNCTIONS 148
BASIC NOTATIONS 149
BIBLIOGRAPHY 151
INDEX 157
|
| any_adam_object | 1 |
| author | Holzapfel, Rolf-Peter 1942- |
| author_GND | (DE-588)117712817 |
| author_facet | Holzapfel, Rolf-Peter 1942- |
| author_role | aut |
| author_sort | Holzapfel, Rolf-Peter 1942- |
| author_variant | r p h rph |
| building | Verbundindex |
| bvnumber | BV010317090 |
| callnumber-first | Q - Science |
| callnumber-label | QA565 |
| callnumber-raw | QA565 |
| callnumber-search | QA565 |
| callnumber-sort | QA 3565 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 240 SK 750 |
| classification_tum | MAT 001f |
| ctrlnum | (OCoLC)32779342 (DE-599)BVBBV010317090 |
| dewey-full | 516.3/5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/5 |
| dewey-search | 516.3/5 |
| dewey-sort | 3516.3 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T17:50:24Z |
| institution | BVB |
| isbn | 3764328355 0817628355 |
| language | English |
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| spelling | Holzapfel, Rolf-Peter 1942- Verfasser (DE-588)117712817 aut The ball and some Hilbert problems Rolf-Peter Holzapfel Basel [u.a.] Birkhäuser 1995 VI, 160 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lectures in mathematics Boule unité ram Courbes elliptiques ram Hilberts twaalfde probleem gtt Picard, schémas de ram Curves, Elliptic Picard schemes Unit ball Einheitskugel (DE-588)4151312-5 gnd rswk-swf Hilbertsche Probleme (DE-588)4159859-3 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Kugel (DE-588)4165914-4 gnd rswk-swf Hilbertsche Probleme (DE-588)4159859-3 s Kugel (DE-588)4165914-4 s DE-604 Einheitskugel (DE-588)4151312-5 s Algebraische Geometrie (DE-588)4001161-6 s GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006865109&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Holzapfel, Rolf-Peter 1942- The ball and some Hilbert problems Boule unité ram Courbes elliptiques ram Hilberts twaalfde probleem gtt Picard, schémas de ram Curves, Elliptic Picard schemes Unit ball Einheitskugel (DE-588)4151312-5 gnd Hilbertsche Probleme (DE-588)4159859-3 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Kugel (DE-588)4165914-4 gnd |
| subject_GND | (DE-588)4151312-5 (DE-588)4159859-3 (DE-588)4001161-6 (DE-588)4165914-4 |
| title | The ball and some Hilbert problems |
| title_auth | The ball and some Hilbert problems |
| title_exact_search | The ball and some Hilbert problems |
| title_full | The ball and some Hilbert problems Rolf-Peter Holzapfel |
| title_fullStr | The ball and some Hilbert problems Rolf-Peter Holzapfel |
| title_full_unstemmed | The ball and some Hilbert problems Rolf-Peter Holzapfel |
| title_short | The ball and some Hilbert problems |
| title_sort | the ball and some hilbert problems |
| topic | Boule unité ram Courbes elliptiques ram Hilberts twaalfde probleem gtt Picard, schémas de ram Curves, Elliptic Picard schemes Unit ball Einheitskugel (DE-588)4151312-5 gnd Hilbertsche Probleme (DE-588)4159859-3 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Kugel (DE-588)4165914-4 gnd |
| topic_facet | Boule unité Courbes elliptiques Hilberts twaalfde probleem Picard, schémas de Curves, Elliptic Picard schemes Unit ball Einheitskugel Hilbertsche Probleme Algebraische Geometrie Kugel |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006865109&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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