Diophantine approximation and Abelian varieties: introductory lectures
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1993
|
| Schriftenreihe: | Lecture notes in mathematics
1566 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 127 S. |
| ISBN: | 3540575286 0387575286 |
Internformat
MARC
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| 245 | 1 | 0 | |a Diophantine approximation and Abelian varieties |b introductory lectures |c B. Edixhoven ... (eds.) |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1993 | |
| 300 | |a XII, 127 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1566 | |
| 650 | 4 | |a Abelian varieties |x Congresses | |
| 650 | 4 | |a Diophantine approximation |x Congresses | |
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| 650 | 0 | 7 | |a Diophantische Approximation |0 (DE-588)4135760-7 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1805082759597654016 |
|---|---|
| adam_text |
Contents
Preface
v
List of Contributors
ix
Introduction
x
Terminology and Prerequisites
xiii
I Diophantine Equations and Approximation,
by
F. Beukers
1
1
Heights
. 1
2
The Subspace Theorem
. 2
3
Weil Functions
. 5
4
Vojta's Conjecture
. 5
5
Results
. 9
II Diophantine Approximation and its Applications,
by R. TlJDEMAN
13
1
Upper Bounds for Approximations
. 13
2
Lower Bounds for Approximations
. 15
3
Applications to Diophantine Equations
. 17
III Roth's Theorem,
by R.
Tijdeman
21
1
The Proof
. 21
2
Variations and Generalisations
. 29
IV The Subspace Theorem of W.M. Schmidt,
by J.H. EVERTSE
31
1
Introduction
. 31
2
Applications
. 33
3
About the Proof of the Subspace theorem
. 37
V Heights on Abelian Varieties,
by J.
Huisman
51
1
Height on
Projective
Space
. 51
2
Heights on
Projective
Varieties
. 52
3
Heights on Abelian Varieties
. 55
4
Metrized Line Bundles
. 58
VI D. Mumford's "A Remark on Mordell's Conjecture",
by J. Top
63
1
Definitions
. 63
2
Mumford's Inequality
. 64
3
Interpretation, Consequences and an Example
. 64
4
The Proof assuming some Properties of Divisor Classes
. 65
5
Proof of the Divisorial Properties
. 66
6
Effectiveness and Generalizations
. 67
VII
Ample Line Bundles and Intersection Theory,
by A.J.
de Jong
69
1
Introduction
. 69
2
Coherent Sheaves, etc
. 69
3
Ample and Very Ample Line Bundles
. 71
4
Intersection Numbers
. 71
5
Numerical Equivalence and Ample Line Bundles
. 74
6
Lemmas to be used in the Proof of Thm. I of Faltings
. 75
Vm The Product Theorem,
by M. van
der
Рит
77
1
Differential Operators and Index
. 77
2
The Product Theorem
. 79
3
From the Product Theorem to Roth's Lemma
. 81
ГХ
Geometric Part of Faltings's Proof,
by C. Faber
83
X Faltings's Version of Siegel's Lemma,
by R.J. Kooman
93
XI Arithmetic Part of Faltings's Proof,
by B. Edixhoven
97
1
Introduction
.97
2
Construction of Proper Models
.97
3
Applying Faltings's version of Siegel's Lemma
.98
4
Leading Terms and Differential Operators
.103
5
Proof of the Main Theorem
.105
XII
Points of Degree
d
on Curves over Number Fields,
by G. van
der Geer
111
ХІП
"The" General Case of S. Lang's Conjecture (after Faltings),
by F. Oort
117
1
The Special Subset of a Variety
.117
2
The Special Subset of a Subvariety of an Abelian Variety
.119
3
The Arithmetic Case
.121
4
Related Conjectures and Results
.121
Bibliography
123 |
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| spelling | Diophantine approximation and Abelian varieties introductory lectures B. Edixhoven ... (eds.) Berlin [u.a.] Springer 1993 XII, 127 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1566 Abelian varieties Congresses Diophantine approximation Congresses Abelsche Mannigfaltigkeit (DE-588)4140992-9 gnd rswk-swf Diophantische Approximation (DE-588)4135760-7 gnd rswk-swf (DE-588)1071861417 Konferenzschrift gnd-content Abelsche Mannigfaltigkeit (DE-588)4140992-9 s Diophantische Approximation (DE-588)4135760-7 s DE-604 Edixhoven, Bas 1962- Sonstige (DE-588)101493740X oth Lecture notes in mathematics 1566 (DE-604)BV000676446 1566 Digitalisierung TU Muenchen application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005492614&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Diophantine approximation and Abelian varieties introductory lectures Lecture notes in mathematics Abelian varieties Congresses Diophantine approximation Congresses Abelsche Mannigfaltigkeit (DE-588)4140992-9 gnd Diophantische Approximation (DE-588)4135760-7 gnd |
| subject_GND | (DE-588)4140992-9 (DE-588)4135760-7 (DE-588)1071861417 |
| title | Diophantine approximation and Abelian varieties introductory lectures |
| title_auth | Diophantine approximation and Abelian varieties introductory lectures |
| title_exact_search | Diophantine approximation and Abelian varieties introductory lectures |
| title_full | Diophantine approximation and Abelian varieties introductory lectures B. Edixhoven ... (eds.) |
| title_fullStr | Diophantine approximation and Abelian varieties introductory lectures B. Edixhoven ... (eds.) |
| title_full_unstemmed | Diophantine approximation and Abelian varieties introductory lectures B. Edixhoven ... (eds.) |
| title_short | Diophantine approximation and Abelian varieties |
| title_sort | diophantine approximation and abelian varieties introductory lectures |
| title_sub | introductory lectures |
| topic | Abelian varieties Congresses Diophantine approximation Congresses Abelsche Mannigfaltigkeit (DE-588)4140992-9 gnd Diophantische Approximation (DE-588)4135760-7 gnd |
| topic_facet | Abelian varieties Congresses Diophantine approximation Congresses Abelsche Mannigfaltigkeit Diophantische Approximation Konferenzschrift |
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