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Heights in Diophantine Geometry - Enrico Bombieri, Walter Gubler

Heights in Diophantine Geometry

Buch | Hardcover
668 Seiten
2006
Cambridge University Press (Verlag)
978-0-521-84615-8 (ISBN)
CHF 129,95 inkl. MwSt
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Diophantine geometry has been studied by number theorists for thousands of years, this monograph is a bridge between the classical theory and modern approach via arithmetic geometry. The treatment is largely self-contained, with proofs given in full detail. Many results appear here for the first time.
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.

Professor Enrico Bombieri is a Professor of Mathematics at the Institute for Advanced Study. Dr Walter Gubler is a Lecturer in Mathematics at the University of Dortmund.

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.

Erscheint lt. Verlag 19.1.2006
Reihe/Serie New Mathematical Monographs
Verlagsort Cambridge
Sprache englisch
Maße 163 x 235 mm
Gewicht 1043 g
Themenwelt Mathematik / Informatik Mathematik Arithmetik / Zahlentheorie
Mathematik / Informatik Mathematik Geometrie / Topologie
ISBN-10 0-521-84615-3 / 0521846153
ISBN-13 978-0-521-84615-8 / 9780521846158
Zustand Neuware
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