"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"--
Author(s): Hideaki Ikoma;Shu Kawaguchi; Atsushi Moriwaki
Series: Cambridge Tracts in Mathematics 226
Publisher: CUP
Year: 2022
Language: English
Commentary: japanese edition : 9D07E15A7FCFB9B1F597CC9F3E6C7836
Pages: 169
Contents
Preface
1 - What Is the Mordell Conjecture (Faltings’s Theorem)?
2 - Some Basics of Algebraic Number Theory
3 - Theory of Heights
4 - Preliminaries for the Proof
of Faltings’s Theorem
5 - The Proof of Faltings’s Theorem
References
Notation
Index of Symbols
Index