Heights in Diophantine Geometry
£65.99
Part of New Mathematical Monographs
- Authors:
- Enrico Bombieri, Institute for Advanced Study, Princeton, New Jersey
- Walter Gubler, Universität Dortmund
- Date Published: September 2007
- availability: Available
- format: Paperback
- isbn: 9780521712293
£
65.99
Paperback
Other available formats:
eBook
Looking for an inspection copy?
This title is not currently available on inspection
-
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.
Read more- 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
Awards
- Enrico Bombieri and Walter Gubler are winners of the American Mathematical Society Joseph Doob Prize for their book Heights in Diophantine Geometry
Reviews & endorsements
'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
See more reviews'The quality of exposition is exemplary, which is not surprising, given the brilliant expository style of the elder author.' Yuri Bilu, Mathematical Review
'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
'…a fundamental and pioneering standard text in the field, which will undoubtedly serve as a basic source for the future development of number theory and arithmetic geometry as a whole.' Werner Kleinert, Zentralblatt MATH
'… remarkable …' European Mathematical Society Newsletter
Customer reviews
Not yet reviewed
Be the first to review
Review was not posted due to profanity
×Product details
- Date Published: September 2007
- format: Paperback
- isbn: 9780521712293
- length: 670 pages
- dimensions: 227 x 155 x 32 mm
- weight: 0.88kg
- availability: 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.
Related Books
related journals
also by this author
Sorry, this resource is locked
Please register or sign in to request access. If you are having problems accessing these resources please email [email protected]
Register Sign in» Proceed
You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.
Continue ×Are you sure you want to delete your account?
This cannot be undone.
Thank you for your feedback which will help us improve our service.
If you requested a response, we will make sure to get back to you shortly.
×