G-functions and geometry: a publication of the Max-Planck-Institut für Mathematik, Bonn
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Braunschweig u.a.
Vieweg
1989
|
| Series: | Aspects of mathematics / E.
13. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 220 - 224 |
| Physical Description: | XII, 229 S. |
| ISBN: | 3528063173 |
Staff View
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| 245 | 1 | 0 | |a G-functions and geometry |b a publication of the Max-Planck-Institut für Mathematik, Bonn |c Yves André. Advisor: Friedrich Hirzebruch |
| 264 | 1 | |a Braunschweig u.a. |b Vieweg |c 1989 | |
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| 490 | 1 | |a Aspects of mathematics / E. |v 13. | |
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Record in the Search Index
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|---|---|
| adam_text | VI
Contents
Logical dependence of the chapters IX
Notations X
Introduction 1
Part One: What are G-functions? 11
Chapter I: G-functions 12
1. Heights and sizes 12
2. Radii 18
3. Several variables; diagonalization 20
4. Examples 24
5. Counterexamples 32
Appendix: calculus of factorials 36
Chapter II: Geometric differential equations 38
1. Definition 38
2. Generalization: modules with connection arising from algebraic geometry .... 40
3. Solutions of geometric differential equations; algebraic structure 43
Part Two: G-functions and differential equations 45
Chapter III: Fuchsian differential systems: formal theory 46
1. Logarithmic singularities 46
2. The language of 9-modules 48
3. Special changes of basis 51
4. Blow-up 53
5. Formal Frobenius and Christol functors 55
Appendix: a zero estimate 58
Chapter IV: Fuchsian differential systems: arithmetic theory 61
1. Background of p-adic analysis 61
2. p-adic differential systems 64
3. Global radius of a 9-module over K (x) 69
4. Size of a d-module 71
5. G-operators (p(A) and a(A)) 74
Appendix: outline of a theorem of Dwork-Robba 85
Contents VII
Chapter V: Local methods 87
1. Resolution of apparent singularities 87
2. Analytic Frobenius functor 89
3. Inversion of the Frobenius functor 92
4. Convergence of the uniform part 98
5. From p(A) to p(Y) 101
6. From p (Y) to a (Y) 103
Appendix: the geometric situation 110
Chapter VI: Global methods 112
1. Iterating A 112
2. Non-vanishing of a crucial determinant 114
3. Hermite-Pade approximants 119
4. From a (y) to a (A) 120
5. Main theorem 124
Part Three: Diophantine questions 127
Chapter VII: Independence of values of G-functions 128
1. Introduction 128
2. Approximating forms 130
3. A method of Gel fond 131
4. Local dependence 134
5. Global dependence; Hasse s principle 139
6. Application to diophantine equations 140
Appendix: on Runge s method 145
Chapter VIII: A criterium of rationality 147
1. Statement of the results 147
2. Approximating forms 155
3. A method of Gel fond 156
4. Application: the isogeny theorem, after Chudnovsky 158
Part Four: G-functions in arithmetic algebraic geometry 162
Chapter IX: Towards Grothendieck s conjecture on periods of
algebraic manifolds 163
1. Periods 163
2. Hodge cycles and period relations 168
3. Period relations: the relative case 173
4. Periods and G-functions 184
5. Conclusion 193
Appendix: special Mumford-Tate groups and absolute Hodge cycles 196
VIII Contents
Chapter X: Endomorphisms in the fibers of an Abelian pencil 200
1. Introduction: distribution of the exceptional fibers 200
2. Period relations on exceptional fibers 203
3. Constructing non-trivial global relations 209
4. Special points on Shimura varieties and other comments 214
Appendix: anew proof of the transcendence of tt 217
Bibliography 220
Index 225
Glossary of notations 228
|
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| dewey-full | 516.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.35 |
| dewey-search | 516.35 |
| dewey-sort | 3516.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV001804210 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:36:11Z |
| institution | BVB |
| isbn | 3528063173 |
| language | English |
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| physical | XII, 229 S. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
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| publisher | Vieweg |
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| series2 | Aspects of mathematics / E. |
| spelling | André, Yves 1959- Verfasser (DE-588)142060895 aut G-functions and geometry a publication of the Max-Planck-Institut für Mathematik, Bonn Yves André. Advisor: Friedrich Hirzebruch Braunschweig u.a. Vieweg 1989 XII, 229 S. txt rdacontent n rdamedia nc rdacarrier Aspects of mathematics / E. 13. Literaturverz. S. 220 - 224 G-Funktion (DE-588)4210136-0 gnd rswk-swf G-Funktion (DE-588)4210136-0 s DE-604 E. Aspects of mathematics 13. (DE-604)BV000018737 13. HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001211527&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | André, Yves 1959- G-functions and geometry a publication of the Max-Planck-Institut für Mathematik, Bonn G-Funktion (DE-588)4210136-0 gnd |
| subject_GND | (DE-588)4210136-0 |
| title | G-functions and geometry a publication of the Max-Planck-Institut für Mathematik, Bonn |
| title_auth | G-functions and geometry a publication of the Max-Planck-Institut für Mathematik, Bonn |
| title_exact_search | G-functions and geometry a publication of the Max-Planck-Institut für Mathematik, Bonn |
| title_full | G-functions and geometry a publication of the Max-Planck-Institut für Mathematik, Bonn Yves André. Advisor: Friedrich Hirzebruch |
| title_fullStr | G-functions and geometry a publication of the Max-Planck-Institut für Mathematik, Bonn Yves André. Advisor: Friedrich Hirzebruch |
| title_full_unstemmed | G-functions and geometry a publication of the Max-Planck-Institut für Mathematik, Bonn Yves André. Advisor: Friedrich Hirzebruch |
| title_short | G-functions and geometry |
| title_sort | g functions and geometry a publication of the max planck institut fur mathematik bonn |
| title_sub | a publication of the Max-Planck-Institut für Mathematik, Bonn |
| topic | G-Funktion (DE-588)4210136-0 gnd |
| topic_facet | G-Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001211527&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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