Heights in Diophantine Geometry

ISBN-13: 9780521712293 / Angielski / Miękka / 2007 / 670 str.

Walter Gubler

Opis

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 provide 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.

Recenzje

'… remarkable …' European Mathematical Society Newsletter

Spis treści

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.