Logarithmic forms and diophantine geometry

著者

• Baker, Alan
• Wüstholz, Gisbert

書誌事項

Logarithmic forms and diophantine geometry

A. Baker, G. Wüstholz

（New mathematical monographs, 9）

Cambridge University Press, 2007

注記

Includes bibliographical references (p. 178-193) and index

内容説明・目次

内容説明

There is now much interplay between studies on logarithmic forms and deep aspects of arithmetic algebraic geometry. New light has been shed, for instance, on the famous conjectures of Tate and Shafarevich relating to abelian varieties and the associated celebrated discoveries of Faltings establishing the Mordell conjecture. This book gives an account of the theory of linear forms in the logarithms of algebraic numbers with special emphasis on the important developments of the past twenty-five years. The first part covers basic material in transcendental number theory but with a modern perspective. The remainder assumes some background in Lie algebras and group varieties, and covers, in some instances for the first time in book form, several advanced topics. The final chapter summarises other aspects of Diophantine geometry including hypergeometric theory and the Andre-Oort conjecture. A comprehensive bibliography rounds off this definitive survey of effective methods in Diophantine geometry.

目次

• Preface. 1. Transcendence origins
• 2. Logarithmic forms
• 3. Diophantine problems
• 4. Commutative algebraic groups
• 5. Multiplicity estimates
• 6. The analytic subgroup theorem
• 7. The quantitative theory
• 8. Further aspects of Diophantine geometry
• Bibliography
• Index.

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BA84556751
• ISBN:
  • 9780521882682
• 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
• ページ数/冊数: x, 198 p.
• 大きさ: 24 cm
• 親書誌ID:
  • BA65869793