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2 results

The Mordell Conjecture
  • A Complete Proof from Diophantine Geometry
  • Hideaki Ikoma, Shu Kawaguchi, Atsushi Moriwaki
  • Published online:
    13 January 2022
    Print publication:
    03 February 2022
  • 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.

  • On Vojta's 1 + Ɛ Conjecture

  • Xi Chen
  • Journal:
    Canadian Journal of Mathematics / Volume 63 / Issue 1 / 01 February 2011
    Published online by Cambridge University Press:
    20 November 2018, pp. 86-103
    Print publication:
    01 February 2011
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  • We give another proof of Vojta's $1\,+\,\varepsilon $ conjecture.