A conjecture on rational approximations to rational points

David McKinnon

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A conjecture on rational approximations to rational points

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arxiv math/0504303 v2 pith:5JQSD7U7 submitted 2005-04-14 math.NT math.AG

A conjecture on rational approximations to rational points

David McKinnon This is my paper

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keywords rationalconjectureapproximationscurveexamplespointsalgebraicalong

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In this paper, we examine how well a rational point P on an algebraic variety X can be approximated by other rational points. We conjecture that if P lies on a rational curve, then the best approximations to P on X can be chosen to lie along a rational curve. We prove this conjecture for a wide range of examples, and for a great many more examples we deduce our conjecture from Vojta's Main Conjecture.

A conjecture on rational approximations to rational points

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