Heights in Diophantine Geometry

Häftad, Engelska, 2007

Del 4 i serien New Mathematical Monographs

916 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2007-09-06
Mått:155 x 227 x 32 mm
Vikt:880 g
Format:Häftad
Språk:Engelska
Serie:New Mathematical Monographs
Antal sidor:670
Förlag:Cambridge University Press
ISBN:9780521712293

Utforska kategorier

Talteori inom Naturvetenskap och teknik
Matematik inom Naturvetenskap och teknik

Mer om författaren

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.

Recensioner i media

'This monograph is a bridge between the classical theory and a modern approach via arithmetic geometry. The authors aim to 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.' L'enseignement mathematique

Innehållsförteckning

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.