Heights in diophantine geometry
著者
書誌事項
Heights in diophantine geometry
（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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