The Mordell Conjecture

Erscheinungsjahr 2022
ISBN: 978-1-108-84595-3
Verlag: Cambridge University Press

Buch, Englisch, Band 226, 150 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 417 g

Reihe: Cambridge Tracts in Mathematics

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.

Autoren/Hrsg.

Ikoma, Hideaki

Kawaguchi, Shu

Moriwaki, Atsushi

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

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.

Über Autor(innen)

Moriwaki, Atsushi
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.

Ikoma, Hideaki
Hideaki Ikoma is Lecturer in the Faculty of Education at Shitennoji University.

Kawaguchi, Shu
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.