Mordell Conjecture

A Complete Proof from Diophantine Geometry

Inbunden, Engelska, 2022

Av Hideaki Ikoma, Shu Kawaguchi, Atsushi Moriwaki, Kyoto) Kawaguchi, Shu (Doshisha University, Japan) Moriwaki, Atsushi (Kyoto University

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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.

Produktinformation

Utgivningsdatum2022-02-03
Mått157 x 235 x 14 mm
Vikt380 g
FormatInbunden
SpråkEngelska
SerieCambridge Tracts in Mathematics
Antal sidor150
FörlagCambridge University Press
ISBN9781108845953

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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.

'This lucid compact book provides a short and direct access to Vojta-Bombieri's proof of Faltings's celebrated theorem. The text itself is mostly self-contained, with all needed results on diophantine geometry presented without unnecessary abstraction, in as concrete a manner as possible. Without doubt, this excellent course will become a standard for anyone wishing to be introduced to the topic of rational points on curves over the rational numbers, and to one of the crowning achievements of the mathematics of our time.' Vincent Maillot, Centre National de la Recherche Scientifique (CNRS), Paris