Roth's theorem for ruled surfaces
Copyright policy )Roth's theorem for ruled surfaces
This paper addresses conjectures of E. Bombieri and P. Vojta in the special case of ruled surfaces not birational to [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /]. Apart from this implicit restriction to [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="02i" /] bundles S over an elliptic curve, the ultimate question of the arithmetic of pairs ( S, D ) for a divisor D requires further restrictions on D which turn the proposed conjectures into the study of Roth's theorem on approximation of algebraic numbers α, but for α now parametrized by an elliptic curve. With these restrictions, best possible answers are obtained. The same study may also be carried out for holomorphic maps, and this is done simultaneously.
Number-theoretic analogues of methods in Nevanlinna theory (work of Vojta et al.), SEMIABELIAN VARIETIES, Settore MAT/03 - GEOMETRIA, Rational and ruled surfaces, INTEGRAL POINTS, SUBVARIETIES, ABELIAN-VARIETIES, Rational points, Value distribution theory in higher dimensions, DIOPHANTINE APPROXIMATION, DIOPHANTINE APPROXIMATION; SEMIABELIAN VARIETIES; ABELIAN-VARIETIES; INTEGRAL POINTS; SUBVARIETIES
Number-theoretic analogues of methods in Nevanlinna theory (work of Vojta et al.), SEMIABELIAN VARIETIES, Settore MAT/03 - GEOMETRIA, Rational and ruled surfaces, INTEGRAL POINTS, SUBVARIETIES, ABELIAN-VARIETIES, Rational points, Value distribution theory in higher dimensions, DIOPHANTINE APPROXIMATION, DIOPHANTINE APPROXIMATION; SEMIABELIAN VARIETIES; ABELIAN-VARIETIES; INTEGRAL POINTS; SUBVARIETIES
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