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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| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2022
|
| Schriftenreihe: | Cambridge tracts in mathematics
226 |
| Links: | https://doi.org/10.1017/9781108991445 |
| 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. |
| Umfang: | 1 Online-Ressource (vii, 169 Seiten) |
| ISBN: | 9781108991445 |
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| 520 | |a 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. | ||
| 700 | 1 | |a Kawaguchi, Shu | |
| 700 | 1 | |a Moriwaki, Atsushi |d 1960- | |
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| spelling | Ikoma, Hideaki 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 c cr Cambridge tracts in mathematics 226 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. Kawaguchi, Shu Moriwaki, Atsushi 1960- Erscheint auch als Druck-Ausgabe 9781108845953 |
| spellingShingle | Ikoma, Hideaki The mordell conjecture a complete proof from diophantine geometry |
| 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_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 | mordell conjecture a complete proof from diophantine geometry |
| title_sub | a complete proof from diophantine geometry |
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