Logarithmic forms and diophantine geometry:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2007
|
| Edition: | 1. publ. |
| Series: | New mathematical monographs
9 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | X, 198 S. |
| ISBN: | 0521882680 9780521882682 |
Staff View
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| 245 | 1 | 0 | |a Logarithmic forms and diophantine geometry |c A. Baker ; G. Wüstholz |
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Record in the Search Index
| _version_ | 1804137203273564160 |
|---|---|
| adam_text | Contents
Preface puge
ix
1
Transcendence
origins I
1.1
Liouville s theorem
1
1.2
The Hermite-Lindemann theorem
5
1.3 The Siegel-Shidlovsky
theory
9
1.4
Siegeľs
lemma
13
1.5
Mahler s method
16
16
Riemann hypothesis over finite fields
20
2
Logarithmic forms
24
2.1
Hubert s seventh problem
24
2.2
The Gelfond-Schneider theorem
25
2.3
The Schneider-Lang theorem
28
2.4
Baker s theorem
32
2.5
The
Δ
-functions
33
2.6
The auxiliary function
36
2.7
Extrapolation
39
2.8
State of the art
41
3
Diophantine problems
46
3.1
Class numbers
46
3.2
The unit equations
49
3.3
The Thue equation
52
3.4
Diophantine curves
54
3.5
Practical computations
57
3.6
Exponential equations
61
3.7
The
дЛосопјесШге
66
vi
Contents
4
Commutative
algebraic groups
70
4.1
Introduction
70
4.2
Basic concepts in algebraic geometry
73
4.3
The groups Ga and Gm
74
4.4
The Lie algebra
76
4.5
Characters
78
4.6
Subgroup varieties
80
4.7
Geometry of Numbers
82
5
Multiplicity estimates
89
5.1
Hubert functions in degree theory
89
5.2
Differential length
93
5.3
Algebraic degree theory
95
5.4
Calculation of the Jacobi rank
97
5.5
The
Wüstholz
theory
101
5.6
Algebraic subgroups of the torus
106
6
The analytic subgroup theorem
109
6.1
Introduction
109
6.2
New applications
117
6.3
Transcendence properties of rational integrals
124
6.4
Algebraic groups and Lie groups
128
6.5
Lindemann s theorem for abelian varieties
131
6.6
Proof of the integral theorem
135
6.7
Extended multiplicity estimates
136
6.8
Proof of the analytic subgroup theorem
140
6.9
Effective constructions on group varieties
145
7
The quantitative theory
149
7.1
Introduction
149
7.2
Sharp estimates for logarithmic forms
150
7.3
Analogues for algebraic groups
154
7.4
Isogeny theorems
158
7.5
Discriminants, polarisations and Galois groups
162
7.6
The Mordell and
Tate
conjectures
165
8
Further aspects of Diophantine geometry
167
8.1
Introduction
167
8.2
The Schmidt subspace theorem
167
8.3
Faltings product theorem
170
8.4
The
André-Oort
conjecture
171
Contents
8.5 Hypergeometric
functions
173
8.6 The Manin-Mumford
conjecture
176
References
178
Index
194
|
| adam_txt |
Contents
Preface puge
ix
1
Transcendence
origins I
1.1
Liouville's theorem
1
1.2
The Hermite-Lindemann theorem
5
1.3 The Siegel-Shidlovsky
theory
9
1.4
Siegeľs
lemma
13
1.5
Mahler's method
16
16
Riemann hypothesis over finite fields
20
2
Logarithmic forms
24
2.1
Hubert's seventh problem
24
2.2
The Gelfond-Schneider theorem
25
2.3
The Schneider-Lang theorem
28
2.4
Baker's theorem
32
2.5
The
Δ
-functions
33
2.6
The auxiliary function
36
2.7
Extrapolation
39
2.8
State of the art
41
3
Diophantine problems
46
3.1
Class numbers
46
3.2
The unit equations
49
3.3
The Thue equation
52
3.4
Diophantine curves
54
3.5
Practical computations
57
3.6
Exponential equations
61
3.7
The
дЛосопјесШге
66
vi
Contents
4
Commutative
algebraic groups
70
4.1
Introduction
70
4.2
Basic concepts in algebraic geometry
73
4.3
The groups Ga and Gm
74
4.4
The Lie algebra
76
4.5
Characters
78
4.6
Subgroup varieties
80
4.7
Geometry of Numbers
82
5
Multiplicity estimates
89
5.1
Hubert functions in degree theory
89
5.2
Differential length
93
5.3
Algebraic degree theory
95
5.4
Calculation of the Jacobi rank
97
5.5
The
Wüstholz
theory
101
5.6
Algebraic subgroups of the torus
106
6
The analytic subgroup theorem
109
6.1
Introduction
109
6.2
New applications
117
6.3
Transcendence properties of rational integrals
124
6.4
Algebraic groups and Lie groups
128
6.5
Lindemann's theorem for abelian varieties
131
6.6
Proof of the integral theorem
135
6.7
Extended multiplicity estimates
136
6.8
Proof of the analytic subgroup theorem
140
6.9
Effective constructions on group varieties
145
7
The quantitative theory
149
7.1
Introduction
149
7.2
Sharp estimates for logarithmic forms
150
7.3
Analogues for algebraic groups
154
7.4
Isogeny theorems
158
7.5
Discriminants, polarisations and Galois groups
162
7.6
The Mordell and
Tate
conjectures
165
8
Further aspects of Diophantine geometry
167
8.1
Introduction
167
8.2
The Schmidt subspace theorem
167
8.3
Faltings'product theorem
170
8.4
The
André-Oort
conjecture
171
Contents
8.5 Hypergeometric
functions
173
8.6 The Manin-Mumford
conjecture
176
References
178
Index
194 |
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| author | Baker, Alan 1939-2018 Wüstholz, Gisbert 1948- |
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| dewey-ones | 516 - Geometry |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 1. publ. |
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| id | DE-604.BV022958053 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T19:03:36Z |
| indexdate | 2024-07-09T21:08:34Z |
| institution | BVB |
| isbn | 0521882680 9780521882682 |
| language | English |
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| spelling | Baker, Alan 1939-2018 Verfasser (DE-588)134145275 aut Logarithmic forms and diophantine geometry A. Baker ; G. Wüstholz 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2007 X, 198 S. txt rdacontent n rdamedia nc rdacarrier New mathematical monographs 9 Includes bibliographical references and index Arithmetical algebraic geometry Logarithms Diophantische Geometrie (DE-588)4150021-0 gnd rswk-swf Arithmetische Geometrie (DE-588)4131383-5 gnd rswk-swf Logarithmus (DE-588)4168047-9 gnd rswk-swf Diophantische Geometrie (DE-588)4150021-0 s DE-604 Arithmetische Geometrie (DE-588)4131383-5 s Logarithmus (DE-588)4168047-9 s Wüstholz, Gisbert 1948- Verfasser (DE-588)129338710 aut New mathematical monographs 9 (DE-604)BV035420183 9 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016162459&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Baker, Alan 1939-2018 Wüstholz, Gisbert 1948- Logarithmic forms and diophantine geometry New mathematical monographs Arithmetical algebraic geometry Logarithms Diophantische Geometrie (DE-588)4150021-0 gnd Arithmetische Geometrie (DE-588)4131383-5 gnd Logarithmus (DE-588)4168047-9 gnd |
| subject_GND | (DE-588)4150021-0 (DE-588)4131383-5 (DE-588)4168047-9 |
| title | Logarithmic forms and diophantine geometry |
| title_auth | Logarithmic forms and diophantine geometry |
| title_exact_search | Logarithmic forms and diophantine geometry |
| title_exact_search_txtP | Logarithmic forms and diophantine geometry |
| title_full | Logarithmic forms and diophantine geometry A. Baker ; G. Wüstholz |
| title_fullStr | Logarithmic forms and diophantine geometry A. Baker ; G. Wüstholz |
| title_full_unstemmed | Logarithmic forms and diophantine geometry A. Baker ; G. Wüstholz |
| title_short | Logarithmic forms and diophantine geometry |
| title_sort | logarithmic forms and diophantine geometry |
| topic | Arithmetical algebraic geometry Logarithms Diophantische Geometrie (DE-588)4150021-0 gnd Arithmetische Geometrie (DE-588)4131383-5 gnd Logarithmus (DE-588)4168047-9 gnd |
| topic_facet | Arithmetical algebraic geometry Logarithms Diophantische Geometrie Arithmetische Geometrie Logarithmus |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016162459&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035420183 |
| work_keys_str_mv | AT bakeralan logarithmicformsanddiophantinegeometry AT wustholzgisbert logarithmicformsanddiophantinegeometry |