The mordell conjecture : a complete proof from Diophantine geometry

書誌事項

The mordell conjecture : a complete proof from Diophantine geometry

Hideaki Ikoma, Shu Kawaguchi, Atsushi Moriwaki

(Cambridge tracts in mathematics, 226)

Cambridge University Press, 2022

  • : hardback

大学図書館所蔵 件 / 19

この図書・雑誌をさがす

注記

Includes bibliographical references (p. 160-162) and indexes

内容説明・目次

内容説明

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.

目次

  • 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.

「Nielsen BookData」 より

関連文献: 1件中  1-1を表示

詳細情報

  • NII書誌ID(NCID)
    BC12842410
  • ISBN
    • 9781108845953
  • LCCN
    2021024960
  • 出版国コード
    uk
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    Cambridge, U.K.
  • ページ数/冊数
    vii, 169 p.
  • 大きさ
    24 cm
  • 分類
  • 件名
  • 親書誌ID
ページトップへ