A conjecture on rational approximations to rational points

Details A conjecture on rational approximations to rational points A conjecture on rational approximations to rational points

2005-04-14

arxiv.org/abs/math/0504303v2

Mathematics

Number Theory

49 pages, 3 figures. Exposition improved, particularly in the proofs of the main theorems, and the connection with accumulatin

Scientific paper

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.

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