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A conjecture on rational approximations to rational points
Author(s):
David
McKinnon
Journal:
J. Algebraic Geom.
16
(2007),
257-303.
Posted:
November 8, 2006
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Abstract |
References |
Additional information
Abstract:
In this paper, we examine how well a rational point  on an algebraic variety  can be approximated by other rational points. We conjecture that if  lies on a rational curve, then the best approximations to  on  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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Additional Information:
David
McKinnon
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, ON N2L 3G1 Canada
Email:
dmckinnon@math.uwaterloo.ca
PII:
S 1056-3911(06)00458-9
Received by editor(s):
May 16, 2005
Received by editor(s) in revised form:
April 24, 2006
Posted:
November 8, 2006
Additional Notes:
This research was supported in part by NSERC grant 250196-02
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