Lang, Serge Diophantine geometry. (English) Zbl 0115.38701 Interscience Tracts in Pure and Applied Mathematics. 11. New York and London: Interscience Publishers, a division of John Wiley and Sons. x, 170 pp. (1962). Reviewer: J. W. S. Cassels Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 8 ReviewsCited in 87 Documents MSC: 11Gxx Arithmetic algebraic geometry (Diophantine geometry) 14Gxx Arithmetic problems in algebraic geometry; Diophantine geometry 11-02 Research exposition (monographs, survey articles) pertaining to number theory 14-02 Research exposition (monographs, survey articles) pertaining to algebraic geometry 11G10 Abelian varieties of dimension \(> 1\) 11G50 Heights 14G40 Arithmetic varieties and schemes; Arakelov theory; heights 14K15 Arithmetic ground fields for abelian varieties 11D41 Higher degree equations; Fermat’s equation 14G05 Rational points 12E25 Hilbertian fields; Hilbert’s irreducibility theorem Keywords:Diophantine geometry; abelian varieties; Roth theorem; heights of points of varieties; Mordell-Weil theorem; Severi-Néron theorem; Thue-Siegel-Roth theorem; Siegel’s theorem; Hilbert’s irreducibility theorem Citations:Zbl 0095.15301; Zbl 0098.13201; Zbl 0099.16103; Zbl 0077.04703; Zbl 0098.26304; JFM 56.0180.05; Zbl 0118.01902 PDF BibTeX XML OpenURL