The Mordell Conjecture: A Complete Proof from Diophantine Geometry

The Mordell conjecture is a significant achievement 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 conjecture, acting as a concise introduction to Diophantine geometry. It will be valuable to advanced undergraduate and graduate students, researchers, and scholars interested in Diophantine geometry.

Format: Hardback
Length: 150 pages
Publication date: 03 February 2022
Publisher: Cambridge University Press

The Mordell conjecture, also known as Faltings' theorem, stands as one of the most significant accomplishments in Diophantine geometry. It asserts that an algebraic curve of genus at least two possesses a finite number of rational points. This remarkable book offers a comprehensive and intricate proof of the Mordell conjecture, following the groundbreaking papers of Bombieri and Vojta. Moreover, it serves as a concise yet comprehensive introduction to Diophantine geometry, beginning with the fundamental concepts of algebraic number theory and delving into various important theorems and techniques, such as the theory of heights, the Mordell–Weil theorem, Siegel's lemma, and Roth's lemma. The text culminates in the proof of the Mordell conjecture, drawing upon the authors' extensive teaching experience. This book is of immense value to advanced undergraduate and graduate students in algebraic geometry and number theory, as well as researchers with a deep interest in Diophantine geometry as a whole.

Weight: 378g
Dimension: 158 x 234 x 17 (mm)
ISBN-13: 9781108845953
Edition number: New ed