Heights in diophantine geometry

著者

書誌事項

Heights in diophantine geometry

Enrico Bombieri, Walter Gubler

(New mathematical monographs, 4)

Cambridge University Press, 2007

Reprinted with corrections

  • : hbk
  • : pbk

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注記

Includes bibliographical references (p. 620-634) and index

"Reprinted with corrections 2007"--T.p. verso

内容説明・目次

内容説明

Diophantine geometry has been studied by number theorists for thousands of years, since the time of Pythagoras, and has continued to be a rich area of ideas such as Fermat's Last Theorem, and most recently the ABC conjecture. This monograph is a bridge between the classical theory and modern approach via arithmetic geometry. The authors provide a clear path through the subject for graduate students and researchers. They have re-examined many results and much of the literature, and give a thorough account of several topics at a level not seen before in book form. The treatment is largely self-contained, with proofs given in full detail. Many results appear here for the first time. The book concludes with a comprehensive bibliography. It is destined to be a definitive reference on modern diophantine geometry, bringing a new standard of rigor and elegance to the field.

目次

  • 1. Heights
  • 2. Weil heights
  • 3. Linear tori
  • 4. Small points
  • 5. The unit equation
  • 6. Roth's theorem
  • 7. The subspace theorem
  • 8. Abelian varieties
  • 9. Neron-Tate heights
  • 10. The Mordell-Weil theorem
  • 11. Faltings theorem
  • 12. The ABC-conjecture
  • 13. Nevanlinna theory
  • 14. The Vojta conjectures
  • Appendix A. Algebraic geometry
  • Appendix B. Ramification
  • Appendix C. Geometry of numbers
  • Bibliography
  • Glossary of notation
  • Index.

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詳細情報

  • NII書誌ID(NCID)
    BA84286318
  • ISBN
    • 9780521846158
    • 9780521712293
  • 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, UK
  • ページ数/冊数
    xvi, 652 p.
  • 大きさ
    24 cm
  • 分類
  • 件名
  • 親書誌ID
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