1.

Record Nr.

UNINA9910815293003321

Autore

Bombieri Enrico <1940->

Titolo

Heights in diophantine geometry / / Enrico Bombieri, Walter Gubler

Pubbl/distr/stampa

Cambridge, : Cambridge University Press, 2006

ISBN

1-107-15225-9

1-280-43486-4

9786610434862

0-511-18387-9

0-511-13947-0

0-511-14061-4

0-511-30918-X

0-511-54287-9

0-511-13984-5

Edizione

[1st ed.]

Descrizione fisica

1 online resource (xvi, 652 pages) : digital, PDF file(s)

Collana

New mathematical monographs ; ; 4

Altri autori (Persone)

GublerWalter

Disciplina

516.35

Soggetti

Arithmetical algebraic geometry

Mathematics

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

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.

Sommario/riassunto

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.