Heights in Diophantine Geometry
$141.99 (C)
Part of New Mathematical Monographs
Authors:
 Enrico Bombieri, Institute for Advanced Study, Princeton, New Jersey
 Walter Gubler, Universität Dortmund
 Date Published: February 2006
 availability: Replaced by 9780521712293
 format: Hardback
 isbn: 9780521846158
$141.99 (C)
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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 reexamined 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 selfcontained, with proofs given in full detail.
Read more The authors have reexamined 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 selfcontained: 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
Prizes
 Enrico Bombieri and Walter Gubler are winners of the American Mathematical Society Joseph Doob Prize for their book Heights in Diophantine Geometry
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 CollegeSee more reviews"The quality of exposition is exemplary, which is not surprising, given the brilliant expository style of the elder author."
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×Product details
 Date Published: February 2006
 format: Hardback
 isbn: 9780521846158
 length: 668 pages
 dimensions: 235 x 163 x 39 mm
 weight: 1.043kg
 availability: Replaced by 9780521712293
Table of Contents
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. NeronTate heights
X. The MordellWeil theorem
XI. Faltings theorem
XII. The ABCconjecture
XIII. Nevanlinna theory
XIV. The Vojta conjectures
Appendix A. Algebraic geometry
Appendix B. Ramification
Appendix C. Geometry of numbers
Bibliography
Glossary of notation
Index.