Heights in Diophantine Geometry

Enrico Bombieri, Walter Gubler - Collection New Mathematical Monographs

652 pages, parution le 19/01/2006

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Résumé

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.

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

Sommaire

Heights
Weil heights
Linear tori
Small points
The unit equatio
Roth's theorem
The subspace theorem
Abelian varieties
Neron-tate heights
The Mordell-Weil thereom
Faltings theorem
The ABC-conjecture
Nevanlinna theory
The Vojta conjectures
Appendix A: Algebraic geometry
Appendix B: Ramification
Appendix C: Geometry of numbers
Bibliography
Glossary of notation
Index

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Enrico Bombieri, Walter Gubler
Collection	New Mathematical Monographs
Parution	19/01/2006
Nb. de pages	652
Format	15,5 x 23,5
Couverture	Relié
Poids	1037g
Intérieur	Noir et Blanc
EAN13	9780521846158
ISBN13	978-0-521-84615-8