Heights in Diophantine Geometry

Erscheinungsjahr 2015
ISBN: 978-0-521-71229-3
Verlag: Cambridge University Press

Buch, Englisch, Band 4, 655 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 954 g

Reihe: New Mathematical Monographs

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.

Autoren/Hrsg.

Bombieri, Enrico

Gubler, Walter

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

I. Heights; II. Weil heights; III. Linear tori; IV. Small points; V. The unit equation; VI. Roth's theorem; VII. The subspace theorem; VIII. Abelian varieties; IX. Neron-Tate heights; X. The Mordell-Weil theorem; XI. Faltings theorem; XII. The ABC-conjecture; XIII. Nevanlinna theory; XIV. The Vojta conjectures; Appendix A. Algebraic geometry; Appendix B. Ramification; Appendix C. Geometry of numbers; Bibliography; Glossary of notation; Index.

Über Autor(innen)

Bombieri, Enrico
Professor Enrico Bombieri is a Professor of Mathematics at the Institute for Advanced Study.

Gubler, Walter
Dr Walter Gubler is a Lecturer in Mathematics at the University of Dortmund.