Arithmetic of higher dimensional algebraic varieties:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2004
|
| Series: | Progress in mathematics
226 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | 3-7643-3259-X |
| Physical Description: | XVI, 287 S. |
| ISBN: | 081763259X 376433259x |
Staff View
MARC
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| 245 | 1 | 0 | |a Arithmetic of higher dimensional algebraic varieties |c Bjorn Poonen ... ed. |
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Record in the Search Index
| _version_ | 1804132771570909184 |
|---|---|
| adam_text | CONTENTS
Abstracts xi
Introduction xv
Part I. Expository Articles
Sir Peter Swinnerton Dyer — Diophantine equations: progress and
problems :. 3
1. Introduction 3
2. The Hasse Principle and the Brauer Manin obstruction 6
3. Zeta functions and L series 12
4. Curves 15
5. Generalities about surfaces 19
6. Rational surfaces 20
7. K3 surfaces and Kummer surfaces 27
8. Density of rational points 28
References 32
ROGER Heath Brown — Rational points and analytic number theory .. 37
1. Introduction 37
2. Contributions from analytic number theory 38
3. Potential applications to analytic number theory 40
References 41
David Harari — Weak approximation on algebraic varieties 43
1. Introduction 43
2. Classical results 44
3. Cohomological methods 50
References 57
vi CONTENTS
Emmanuel Peyre — Counting points on varieties using universal torsors
61
1. Introduction 61
2. Heights on projective varieties 63
3. Manin s principle 66
4. Results 70
5. The counterexample of Batyrev and Tschinkel 71
6. Methods of counting 71
7. A basic example 72
8. Universal torsors 73
9. Toric varieties 76
10. The plane blown up in 4 points 78
11. Generalization 79
References 80
Part II. Research Articles
Victor V. Batyrev Oleg N. Popov — The Cox ring of a Del Pezzo
surface 85
1. Introduction 85
2. Del Pezzo surfaces 89
3. Generators of Cox(Xr) 92
4. Quadratic relations in Cox(Xr) 97
References 102
Niklas Broberg Per Salberger — Counting rational points on
threefolds 105
1. Introduction 105
2. Preliminaries 106
3. Proof of the main theorem 112
References 119
Jean Louis Colliot Thelene Philippe Gille — Remarques sur
Vapproximation faible sur un corps de fonctions d une variable 121
1. Introduction 121
2. Rappels : Approximation faible 122
3. Rappels : Cohomologie galoisienne des corps C 123
4. Approximation faible pour les espaces homogenes de groupes lineaires
connexes et pour les varietes qui s y ramenent 124
CONTENTS vii
5. Une surface d Enriques qui ne satisfait pas a l approximation faible
130
References 133
Jordan S. Ellenberg — K3 surfaces over number fields with geometric
Picard number one 135
1. Introduction 135
2. Proofs 136
References 140
Tom Graber, Joseph Harris, Barry Mazur Jason Starr —
Jumps in Mordell Weil rank and Arithmetic Surjectivity 141
1. Arithmetic surjectivity 142
2. Quadratic twist families 144
3. The Cassels Schinzel example 146
References 147
Brendan Hassett Yuri Tschinkel — Universal torsors and Cox
rings 149
1. Introduction 149
2. Generalities on the Cox ring 151
3. Generalities on toric varieties 155
4. The E6 cubic surface 158
5. D4 cubic surface 169
References 172
Bjorn Poonen Jose Felipe Voloch — Random diophantine equations
175
1. Introduction 176
2. A conjecture 176
3. Motivation and evidence 177
4. Generalization to number fields 179
Appendix A. The Brauer Manin obstruction for complete intersections
of dimension 3 (by Jean Louis Colliot Thelene) 180
Appendix B. Applications of the Weak Lefschetz Theorem (by Nicholas
M. Katz) 182
References 183
Wayne Raskind Victor Scharaschkin — Descent on simply connected
surfaces over algebraic number fields 185
viii CONTENTS
1. Introduction 185
2. Notation and preliminaries 187
3. Rapid review of the theory of Colliot Thelene Sansuc 188
4. The homological algebra of descent 190
5. The elementary obstruction 191
6. The Tate conjecture and the Brauer group 194
7. Universal gerbes and the higher Abel Jacobi mapping 196
8. Geometric interpretation of the Brauer Manin obstruction 197
9. Descent on curves 200
10. Concluding remarks 200
Appendix A. Stacks and gerbes 201
Appendix B. Description of the Brauer group in terms of gerbes 202
References 202
Joseph Shalika, Ramin Takloo Bighash Yuri Tschinkel — Rational
points on compactifications of semi simple groups of rank 1 205
1. Introduction 205
2. Basic definitions and results 207
3. Heights and height integrals 210
4. Eisenstein series 212
5. Eisenstein integrals 215
6. P series 218
7. The cuspidal spectrum 224
8. Appendix 227
References 232
Sir Peter Swinnerton Dyer — Weak Approximation on Del Pezzo
surfaces of degree 4 235
1. Introduction 235
2. The Legendre Jacobi functions 237
3. Salberger s device 246
4. Reduction to a pencil of conies 250
5. Proof of Theorem 2 253
References 257
Olivier Wittenberg — Transcendental Brauer Manin obstruction on a
pencil of elliptic curves 259
1. Introduction 259
2. Preliminaries: 2 descent and the Brauer group of an elliptic curve . . 260
3. An actual example 263
CONTENTS ix
References 266
Glossary 269
Index 279
|
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| id | DE-604.BV019345082 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:58:07Z |
| institution | BVB |
| isbn | 081763259X 376433259x |
| language | English |
| lccn | 2003069594 |
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| physical | XVI, 287 S. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Arithmetic of higher dimensional algebraic varieties Bjorn Poonen ... ed. Boston [u.a.] Birkhäuser 2004 XVI, 287 S. txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 226 3-7643-3259-X Variedades algébricas (congressos) larpcal Variétés algébriques Algebraic varieties Algebraische Mannigfaltigkeit (DE-588)4128509-8 gnd rswk-swf Dimension n (DE-588)4309313-9 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content Algebraische Mannigfaltigkeit (DE-588)4128509-8 s Dimension n (DE-588)4309313-9 s DE-604 Poonen, Bjorn Sonstige oth Progress in mathematics 226 (DE-604)BV000004120 226 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012809452&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Arithmetic of higher dimensional algebraic varieties Progress in mathematics Variedades algébricas (congressos) larpcal Variétés algébriques Algebraic varieties Algebraische Mannigfaltigkeit (DE-588)4128509-8 gnd Dimension n (DE-588)4309313-9 gnd |
| subject_GND | (DE-588)4128509-8 (DE-588)4309313-9 (DE-588)4143413-4 |
| title | Arithmetic of higher dimensional algebraic varieties |
| title_auth | Arithmetic of higher dimensional algebraic varieties |
| title_exact_search | Arithmetic of higher dimensional algebraic varieties |
| title_full | Arithmetic of higher dimensional algebraic varieties Bjorn Poonen ... ed. |
| title_fullStr | Arithmetic of higher dimensional algebraic varieties Bjorn Poonen ... ed. |
| title_full_unstemmed | Arithmetic of higher dimensional algebraic varieties Bjorn Poonen ... ed. |
| title_short | Arithmetic of higher dimensional algebraic varieties |
| title_sort | arithmetic of higher dimensional algebraic varieties |
| topic | Variedades algébricas (congressos) larpcal Variétés algébriques Algebraic varieties Algebraische Mannigfaltigkeit (DE-588)4128509-8 gnd Dimension n (DE-588)4309313-9 gnd |
| topic_facet | Variedades algébricas (congressos) Variétés algébriques Algebraic varieties Algebraische Mannigfaltigkeit Dimension n Aufsatzsammlung |
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