Roth's theorem for ruled surfaces

Gasbarri, C. and Mcquillan, M. (2005) Roth's theorem for ruled surfaces. American Journal of Mathematics, 127(3), pp. 471-492.

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Abstract

This paper addresses conjectures of E. Bombieri and P. Vojta in the special case of ruled surfaces not birational to 2. Apart from this implicit restriction to 1 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

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:McQuillan, Dr Michael
Authors: Gasbarri, C., and Mcquillan, M.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:American Journal of Mathematics
ISSN:1582-5329

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
291721Non-Commutative Mori TheoryMichael McQuillanEngineering & Physical Sciences Research Council (EPSRC)GR/A10109/01Physics and Astronomy