Heights in diophantine geometry /
Bombieri, Enrico, 1940-
Heights in diophantine geometry / Enrico Bombieri, Walter Gubler. - Cambridge : Cambridge University Press, 2006. - 1 online resource (xvi, 652 pages) : digital, PDF file(s). - New mathematical monographs ; 4 . - New mathematical monographs ; 4. .
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.
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.
9780511542879 (ebook)
Arithmetical algebraic geometry.
QA242.5 / .B66 2006
516.35
Heights in diophantine geometry / Enrico Bombieri, Walter Gubler. - Cambridge : Cambridge University Press, 2006. - 1 online resource (xvi, 652 pages) : digital, PDF file(s). - New mathematical monographs ; 4 . - New mathematical monographs ; 4. .
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.
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.
9780511542879 (ebook)
Arithmetical algebraic geometry.
QA242.5 / .B66 2006
516.35