The Mordell Conjecture - Hideaki Ikoma, Shu Kawaguchi, Atsushi Moriwaki

The Mordell Conjecture

A Complete Proof from Diophantine Geometry
Buch | Hardcover
150 Seiten
2022
Cambridge University Press (Verlag)
978-1-108-84595-3 (ISBN)
78,55 inkl. MwSt
This book provides a self-contained proof of the Mordell conjecture (Faltings's theorem) - one of the most important achievements in Diophantine geometry - alongside a concise introduction to the field of Diophantine geometry itself, at a level suitable for advanced undergraduate students and graduate students.
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.

Hideaki Ikoma is Lecturer in the Faculty of Education at Shitennoji University. Shu Kawaguchi is Professor in the Department of Mathematical Sciences at Doshisha University. He was awarded the Young Scientists' Prize by the Ministry of Education, Culture, Sports, Science and Technology of Japan in 2010. Atsushi Moriwaki is Professor in the Department of Mathematics at Graduate School of Science, Kyoto University. He is the author of Arakelov Geometry (2014) and co-author of Arakelov Geometry over Adelic Curves (2020), and was awarded the Autumn Prize of the Mathematical society of Japan in 2001.

1. What is the Mordell conjecture?; 2. Some basics of algebraic number theory; 3. Theory of heights; 4. Preliminaries; 5. The proof of Falthing's theorem.

Erscheinungsdatum
Reihe/Serie Cambridge Tracts in Mathematics
Zusatzinfo Worked examples or Exercises
Verlagsort Cambridge
Sprache englisch
Maße 157 x 235 mm
Gewicht 380 g
Themenwelt Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Arithmetik / Zahlentheorie
Mathematik / Informatik Mathematik Geometrie / Topologie
ISBN-10 1-108-84595-9 / 1108845959
ISBN-13 978-1-108-84595-3 / 9781108845953
Zustand Neuware
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