Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

A conjecture on rational approximations to rational points


Author: David McKinnon
Journal: J. Algebraic Geom. 16 (2007), 257-303
DOI: https://doi.org/10.1090/S1056-3911-06-00458-9
Published electronically: November 8, 2006
MathSciNet review: 2274515
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Abstract | References | Additional Information

Abstract: 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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David McKinnon
Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, ON N2L 3G1 Canada
MR Author ID: 667698
Email: dmckinnon@math.uwaterloo.ca

Received by editor(s): May 16, 2005
Received by editor(s) in revised form: April 24, 2006
Published electronically: November 8, 2006
Additional Notes: This research was supported in part by NSERC grant 250196-02