03328nam 2200733Ia 450 991081529300332120200520144314.01-107-15225-91-280-43486-497866104348620-511-18387-90-511-13947-00-511-14061-40-511-30918-X0-511-54287-90-511-13984-5(CKB)1000000000352665(EBL)244411(OCoLC)171137932(SSID)ssj0000170056(PQKBManifestationID)11178766(PQKBTitleCode)TC0000170056(PQKBWorkID)10215237(PQKB)10581221(UkCbUP)CR9780511542879(Au-PeEL)EBL244411(CaPaEBR)ebr10129127(CaONFJC)MIL43486(OCoLC)935228920(MiAaPQ)EBC244411(PPN)190408081(EXLCZ)99100000000035266520050704d2006 uy 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierHeights in diophantine geometry /Enrico Bombieri, Walter Gubler1st ed.Cambridge Cambridge University Press20061 online resource (xvi, 652 pages) digital, PDF file(s)New mathematical monographs ;4Title from publisher's bibliographic system (viewed on 05 Oct 2015).0-521-71229-7 0-521-84615-3 Includes bibliographical references and index.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.New mathematical monographs ;4.Arithmetical algebraic geometryMathematicsArithmetical algebraic geometry.Mathematics.516.35Bombieri Enrico1940-66410Gubler Walter726292MiAaPQMiAaPQMiAaPQBOOK9910815293003321Heights in diophantine geometry1425224UNINA