Rational Points on Algebraic Varieties:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
2001
|
| Schriftenreihe: | Progress in Mathematics
199 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book is devoted to the study of rational and integral points on higher dimensional algebraic varieties. It contains research papers addressing the arithmetic geometry of varieties which are not of general type, with an em phasis on how rational points are distributed with respect to the classical, Zariski and adelic topologies. The book gives a glimpse of the state of the art of this rapidly expanding domain in arithmetic geometry. The techniques involve explicit geometric con structions, ideas from the minimal model program in algebraic geometry as well as analytic number theory and harmonic analysis on adelic groups. In recent years there has been substantial progress in our understanding of the arithmetic of algebraic surfaces. Five papers are devoted to cubic surfaces: Basile and Fisher study the existence of rational points on certain diagonal cubics, Swinnerton-Dyer considers weak approximation and Broberg proves upper bounds on the number of rational points on the complement to lines on cubic surfaces. Peyre and Tschinkel compare numerical data with conjectures concerning asymptotics of rational points of bounded height on diagonal cubics of rank ~ 2. Kanevsky and Manin investigate the composition of points on cubic surfaces. Satge constructs rational curves on certain Kummer surfaces. Colliot-Thelene studies the Hasse principle for pencils of curves of genus 1. In an appendix to this paper Skorobogatov produces explicit examples of Enriques surfaces with a Zariski dense set of rational points |
| Beschreibung: | 1 Online-Ressource (XVI, 446 p) |
| ISBN: | 9783034883689 9783034895361 |
| DOI: | 10.1007/978-3-0348-8368-9 |
Internformat
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| 490 | 0 | |a Progress in Mathematics |v 199 | |
| 500 | |a This book is devoted to the study of rational and integral points on higher dimensional algebraic varieties. It contains research papers addressing the arithmetic geometry of varieties which are not of general type, with an em phasis on how rational points are distributed with respect to the classical, Zariski and adelic topologies. The book gives a glimpse of the state of the art of this rapidly expanding domain in arithmetic geometry. The techniques involve explicit geometric con structions, ideas from the minimal model program in algebraic geometry as well as analytic number theory and harmonic analysis on adelic groups. In recent years there has been substantial progress in our understanding of the arithmetic of algebraic surfaces. Five papers are devoted to cubic surfaces: Basile and Fisher study the existence of rational points on certain diagonal cubics, Swinnerton-Dyer considers weak approximation and Broberg proves upper bounds on the number of rational points on the complement to lines on cubic surfaces. Peyre and Tschinkel compare numerical data with conjectures concerning asymptotics of rational points of bounded height on diagonal cubics of rank ~ 2. Kanevsky and Manin investigate the composition of points on cubic surfaces. Satge constructs rational curves on certain Kummer surfaces. Colliot-Thelene studies the Hasse principle for pencils of curves of genus 1. In an appendix to this paper Skorobogatov produces explicit examples of Enriques surfaces with a Zariski dense set of rational points | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Peyre, Emmanuel |
| author_GND | (DE-588)123243300 (DE-588)129188964 |
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| author_sort | Peyre, Emmanuel |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-8368-9 |
| format | Electronic eBook |
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| id | DE-604.BV042422110 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:10Z |
| institution | BVB |
| isbn | 9783034883689 9783034895361 |
| language | English |
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| spelling | Peyre, Emmanuel Verfasser (DE-588)123243300 aut Rational Points on Algebraic Varieties edited by Emmanuel Peyre, Yuri Tschinkel Basel Birkhäuser Basel 2001 1 Online-Ressource (XVI, 446 p) txt rdacontent c rdamedia cr rdacarrier Progress in Mathematics 199 This book is devoted to the study of rational and integral points on higher dimensional algebraic varieties. It contains research papers addressing the arithmetic geometry of varieties which are not of general type, with an em phasis on how rational points are distributed with respect to the classical, Zariski and adelic topologies. The book gives a glimpse of the state of the art of this rapidly expanding domain in arithmetic geometry. The techniques involve explicit geometric con structions, ideas from the minimal model program in algebraic geometry as well as analytic number theory and harmonic analysis on adelic groups. In recent years there has been substantial progress in our understanding of the arithmetic of algebraic surfaces. Five papers are devoted to cubic surfaces: Basile and Fisher study the existence of rational points on certain diagonal cubics, Swinnerton-Dyer considers weak approximation and Broberg proves upper bounds on the number of rational points on the complement to lines on cubic surfaces. Peyre and Tschinkel compare numerical data with conjectures concerning asymptotics of rational points of bounded height on diagonal cubics of rank ~ 2. Kanevsky and Manin investigate the composition of points on cubic surfaces. Satge constructs rational curves on certain Kummer surfaces. Colliot-Thelene studies the Hasse principle for pencils of curves of genus 1. In an appendix to this paper Skorobogatov produces explicit examples of Enriques surfaces with a Zariski dense set of rational points Mathematics Mathematics, general Mathematik 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 1\p DE-604 Tschinkel, Yuri 1964- Sonstige (DE-588)129188964 oth https://doi.org/10.1007/978-3-0348-8368-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Peyre, Emmanuel Rational Points on Algebraic Varieties Mathematics Mathematics, general Mathematik 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 edited by Emmanuel Peyre, Yuri Tschinkel |
| title_fullStr | Rational Points on Algebraic Varieties edited by Emmanuel Peyre, Yuri Tschinkel |
| title_full_unstemmed | Rational Points on Algebraic Varieties edited by Emmanuel Peyre, Yuri Tschinkel |
| title_short | Rational Points on Algebraic Varieties |
| title_sort | rational points on algebraic varieties |
| topic | Mathematics Mathematics, general Mathematik Rationaler Punkt (DE-588)4177004-3 gnd Algebraische Varietät (DE-588)4581715-7 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Rationaler Punkt Algebraische Varietät |
| url | https://doi.org/10.1007/978-3-0348-8368-9 |
| work_keys_str_mv | AT peyreemmanuel rationalpointsonalgebraicvarieties AT tschinkelyuri rationalpointsonalgebraicvarieties |