The mordell conjecture: a complete proof from diophantine geometry
The Mordell conjecture (Faltings's theorem) is one of the most important achievements in Diophantine geometry, stating that an algebraic curve of genus at least two has only finitely many rational points. This book provides a self-contained and detailed proof of the Mordell conjecture following...
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| Hauptverfasser: | , , |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2022
|
| Schriftenreihe: | Cambridge tracts in mathematics
226 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | The Mordell conjecture (Faltings's theorem) is one of the most important achievements in Diophantine geometry, stating that an algebraic curve of genus at least two has only finitely many rational points. This book provides a self-contained and detailed proof of the Mordell conjecture following the papers of Bombieri and Vojta. Also acting as a concise introduction to Diophantine geometry, the text starts from basics of algebraic number theory, touches on several important theorems and techniques (including the theory of heights, the Mordell-Weil theorem, Siegel's lemma and Roth's lemma) from Diophantine geometry, and culminates in the proof of the Mordell conjecture. Based on the authors' own teaching experience, it will be of great value to advanced undergraduate and graduate students in algebraic geometry and number theory, as well as researchers interested in Diophantine geometry as a whole |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 13 Jan 2022) |
| Beschreibung: | 1 Online-Ressource (vii, 169 Seiten) |
| ISBN: | 9781108991445 |
| DOI: | 10.1017/9781108991445 |
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| author | Ikoma, Hideaki ca. 20./21. Jh Kawaguchi, Shu ca. 20./21. Jh Moriwaki, Atsushi 1960- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| isbn | 9781108991445 |
| language | English |
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| spelling | Ikoma, Hideaki ca. 20./21. Jh. (DE-588)1245441612 aut The mordell conjecture a complete proof from diophantine geometry Hideaki Ikoma, Shitennoji University, Shu Kawaguchi, Doshisha University, Atsushi Moriwaki, Kyoto University Cambridge Cambridge University Press 2022 1 Online-Ressource (vii, 169 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 226 Title from publisher's bibliographic system (viewed on 13 Jan 2022) The Mordell conjecture (Faltings's theorem) is one of the most important achievements in Diophantine geometry, stating that an algebraic curve of genus at least two has only finitely many rational points. This book provides a self-contained and detailed proof of the Mordell conjecture following the papers of Bombieri and Vojta. Also acting as a concise introduction to Diophantine geometry, the text starts from basics of algebraic number theory, touches on several important theorems and techniques (including the theory of heights, the Mordell-Weil theorem, Siegel's lemma and Roth's lemma) from Diophantine geometry, and culminates in the proof of the Mordell conjecture. Based on the authors' own teaching experience, it will be of great value to advanced undergraduate and graduate students in algebraic geometry and number theory, as well as researchers interested in Diophantine geometry as a whole Mordell conjecture Diophantische Geometrie (DE-588)4150021-0 gnd rswk-swf Mordell-Vermutung (DE-588)4123793-6 gnd rswk-swf Mordell-Vermutung (DE-588)4123793-6 s Diophantische Geometrie (DE-588)4150021-0 s DE-604 Kawaguchi, Shu ca. 20./21. Jh. (DE-588)1245442074 aut Moriwaki, Atsushi 1960- (DE-588)1068650419 aut Erscheint auch als Druck-Ausgabe 978-1-108-84595-3 https://doi.org/10.1017/9781108991445 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Ikoma, Hideaki ca. 20./21. Jh Kawaguchi, Shu ca. 20./21. Jh Moriwaki, Atsushi 1960- The mordell conjecture a complete proof from diophantine geometry Mordell conjecture Diophantische Geometrie (DE-588)4150021-0 gnd Mordell-Vermutung (DE-588)4123793-6 gnd |
| subject_GND | (DE-588)4150021-0 (DE-588)4123793-6 |
| title | The mordell conjecture a complete proof from diophantine geometry |
| title_auth | The mordell conjecture a complete proof from diophantine geometry |
| title_exact_search | The mordell conjecture a complete proof from diophantine geometry |
| title_exact_search_txtP | The mordell conjecture a complete proof from diophantine geometry |
| title_full | The mordell conjecture a complete proof from diophantine geometry Hideaki Ikoma, Shitennoji University, Shu Kawaguchi, Doshisha University, Atsushi Moriwaki, Kyoto University |
| title_fullStr | The mordell conjecture a complete proof from diophantine geometry Hideaki Ikoma, Shitennoji University, Shu Kawaguchi, Doshisha University, Atsushi Moriwaki, Kyoto University |
| title_full_unstemmed | The mordell conjecture a complete proof from diophantine geometry Hideaki Ikoma, Shitennoji University, Shu Kawaguchi, Doshisha University, Atsushi Moriwaki, Kyoto University |
| title_short | The mordell conjecture |
| title_sort | the mordell conjecture a complete proof from diophantine geometry |
| title_sub | a complete proof from diophantine geometry |
| topic | Mordell conjecture Diophantische Geometrie (DE-588)4150021-0 gnd Mordell-Vermutung (DE-588)4123793-6 gnd |
| topic_facet | Mordell conjecture Diophantische Geometrie Mordell-Vermutung |
| url | https://doi.org/10.1017/9781108991445 |
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