Heights in Diophantine Geometry
Heights in Diophantine Geometry
Walter Gubler , Universität Dortmund
$91.00
USDDiophantine 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.
- The authors 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
- For graduate students and researchers, and is largely self-contained: proofs are given in full detail, and many results appear here for the first time
- Destined to be a definitive reference on modern diophantine geometry, bringing a new standard of rigour and elegance to the field
Reviews & endorsements
"Bombieri and Gubler have written an excellent introduction to some exciting mathematics...written with an excellent combination of clarity and rigor, with the authors highlighting which parts can be skipped on a first reading and which parts are particularly important for later material. The book also contains a glossary of notation, a good index, and a nice bibliography collecting many of the primary sources in this field."
MAA Reviews, Darren Glass, Gettysburg College
"The quality of exposition is exemplary, which is not surprising, given the brilliant expository style of the elder author."
Yuri Bilu, MATHEMATICAL REVIEWS
Product details
September 2007Paperback
9780521712293
670 pages
227 × 155 × 32 mm
0.88kg
Available
Table of Contents
- 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.
