Rational points on algebraic varieties:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
2001
|
| Series: | Progress in mathematics
199 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XVI, 446 S. graph. Darst. : 24 cm |
| ISBN: | 3764366125 |
Staff View
MARC
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| 245 | 1 | 0 | |a Rational points on algebraic varieties |c Emmanuel Peyre ... ed. |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2001 | |
| 300 | |a XVI, 446 S. |b graph. Darst. : 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Progress in mathematics |v 199 | |
| 500 | |a Literaturangaben | ||
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| 650 | 4 | |a Variétés algébriques | |
| 650 | 4 | |a Algebraic varieties | |
| 650 | 4 | |a Rational points (Geometry) | |
| 650 | 0 | 7 | |a Rationaler Punkt |0 (DE-588)4177004-3 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804128822052782080 |
|---|---|
| adam_text | CONTENTS
Introduction v
Abstracts xi
Carmen Laura Basile Thomas Anthony Fisher — Diagonal cubic
equations in four variables with prime coefficients 1
References 11
Niklas Broberg — Rational points on cubic surfaces 13
Introduction 13
1. Notations and preliminaries 15
2. Ternary quadratic forms 20
3. Proof of the main theorem 28
References 34
Antoine Chambert Loir Yuri Tschinkel — Torseurs arithmetiques
et espaces fibres 37
Introduction 37
Notations et conventions 40
1. Torseurs arithmetiques 40
2. Espaces fibres 51
References 69
Antoine Chambert Loir Yuri Tschinkel — Fonctions zita des
hauteurs des espaces fibres 71
Introduction 71
Notations et conventions 74
3. Fonctions holomorphes dans un tube 75
4. Varietes toriques 87
viii CONTENTS
5. Application aux fibrations en varietes toriques 101
Appendice A. Un theoreme tauberien 107
Appendice B. Demonstration de quelques inegalites 109
References 114
Jean Louis Colliot Thelene — Hasse principle for pencils of curves of
genus one whose Jacobians have a rational 2 division point, close variation
on a paper of Bender and Swinnerton Dyer 117
Statement of the Theorems 119
1. Selmer groups associated to a degree 2 isogeny 125
2. Proof of Theorem A 142
3. Proof of Theorem B 156
References 160
Alexei SKOROBOGATOV — Enriques surfaces with a dense set of rational
points, Appendix to the paper by J. L. Colliot Thelene 163
References 168
Brendan Hassett Yuri Tschinkel — Density of integral points on
algebraic varieties 169
Introduction 169
1. Generalities 171
2. Geometry 172
3. The fibration method and nondegenerate multisections 177
4. Approximation techniques 181
5. Conic bundles and integral points 183
6. Potential density for log K3 surfaces 193
References 195
Dimitri Kanevsky Yuri Manin — Composition of points and the
Mordell Weil problem for cubic surfaces 199
1. Introduction 199
2. Cardinality of generators of subgroups in a reflection group 202
3. Structure of universal equivalence 206
4. A group theoretic description of universal equivalence 208
5. Birationally trivial cubic surfaces: a finiteness theorem 213
References 218
Emmanuel Peyre — Torseurs universels et methode du cercle 221
Introduction 221
CONTENTS ix
1. Une version raffinee d une conjecture de Manin 223
2. Passage au torseur universel 233
3. Intersections completes 254
4. Conclusion 271
References 272
Emmanuel Peyre Yuri Tschinkel— Tamagawa numbers of diagonal
cubic surfaces of higher rank 275
Introduction 275
1. Description of the conjectural constant 277
2. The Galois module Pic(F) 280
3. Euler product for the good places 286
4. Density at the bad places 288
5. The constant a(V) 291
6. Some statistical formulae 297
7. Presentation of the results 298
References 304
B jorn Poonen — The Hasse principle for complete intersections in protective
space 307
References 310
Philippe Satge — Une construction de courbes k rationnelles sur les
surfaces de Kummer d un produit de courbes de genre 1 313
Introduction 313
1. Relevement des courbes de Pi^ x Pi,*, sur la surface de Kummer .. 316
2. Exemples 320
References 333
Matthias Strauch — Arithmetic Stratifications and Partial Eisenstein
Series 335
Introduction 335
1. The fibre bundles: geometric arithmetic preliminaries 338
2. Height zeta functions 342
3. Arithmetic stratification 351
References 355
Sir Peter Swinnerton Dyer — Weak Approximation and R equivalence
on Cubic Surfaces 357
1. Introduction 358
x CONTENTS
2. Geometric background 361
3. Approximation at an infinite prime 370
4. Approximation at a finite prime 371
5. The lifting process 380
6. The dense lifting process 386
7. Adelic results 394
8. Surfaces X? + X$ + X$ dX§ = 0 395
References 403
Trevor D. Wooley — Hua s lemma and exponential sums over binary
forms 405
1. Introduction 405
2. Preliminary reductions 411
3. Integral points on affine plane curves 421
4. The inductive step 430
5. The completion of the proof of Theorem 1.1 441
References 445
|
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| id | DE-604.BV013970009 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:55:21Z |
| institution | BVB |
| isbn | 3764366125 |
| language | English |
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| physical | XVI, 446 S. graph. Darst. : 24 cm |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Rational points on algebraic varieties Emmanuel Peyre ... ed. Basel [u.a.] Birkhäuser 2001 XVI, 446 S. graph. Darst. : 24 cm txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 199 Literaturangaben Points rationnels (Géométrie) Variétés algébriques Algebraic varieties Rational points (Geometry) Rationaler Punkt (DE-588)4177004-3 gnd rswk-swf Algebraische Varietät (DE-588)4581715-7 gnd rswk-swf Algebraische Varietät (DE-588)4581715-7 s Rationaler Punkt (DE-588)4177004-3 s DE-604 Peyre, Emmanuel Sonstige (DE-588)123243300 oth Progress in mathematics 199 (DE-604)BV000004120 199 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009562378&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rational points on algebraic varieties Progress in mathematics Points rationnels (Géométrie) Variétés algébriques Algebraic varieties Rational points (Geometry) Rationaler Punkt (DE-588)4177004-3 gnd Algebraische Varietät (DE-588)4581715-7 gnd |
| subject_GND | (DE-588)4177004-3 (DE-588)4581715-7 |
| title | Rational points on algebraic varieties |
| title_auth | Rational points on algebraic varieties |
| title_exact_search | Rational points on algebraic varieties |
| title_full | Rational points on algebraic varieties Emmanuel Peyre ... ed. |
| title_fullStr | Rational points on algebraic varieties Emmanuel Peyre ... ed. |
| title_full_unstemmed | Rational points on algebraic varieties Emmanuel Peyre ... ed. |
| title_short | Rational points on algebraic varieties |
| title_sort | rational points on algebraic varieties |
| topic | Points rationnels (Géométrie) Variétés algébriques Algebraic varieties Rational points (Geometry) Rationaler Punkt (DE-588)4177004-3 gnd Algebraische Varietät (DE-588)4581715-7 gnd |
| topic_facet | Points rationnels (Géométrie) Variétés algébriques Algebraic varieties Rational points (Geometry) Rationaler Punkt Algebraische Varietät |
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