TY  - BOOK
AU  - Bombieri,Enrico
AU  - Gubler,Walter
ED  - Cambridge eBooks.
TI  - Heights in diophantine geometry
T2  - New mathematical monographs
SN  - 9780511542879 (ebook)
AV  - QA242.5 .B66 2006
U1  - 516.35 22
PY  - 2006///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Arithmetical algebraic geometry
KW  - Electronic books
KW  - local
N1  - Title from publisher's bibliographic system (viewed on 05 Oct 2015); Heights -- Weil heights -- Linear tori -- Small points -- The unit equation -- Roth's theorem -- The subspace theorem -- Abelian varieties -- Neron-Tate heights -- The Mordell-Weil theorem -- Falting's theorem -- The abc-conjecture -- Nevalinna theory -- The Vojta conjectures
N2  - 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
UR  - http://ezproxy.alfaisal.edu/login?url=http://dx.doi.org/10.1017/CBO9780511542879
ER  -