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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Vojta's Main Conjecture for blowup surfaces


Author: David McKinnon
Journal: Proc. Amer. Math. Soc. 131 (2003), 1-12
MSC (2000): Primary 11G05, 11G35, 14G05, 14G40
Published electronically: August 19, 2002
MathSciNet review: 1929015
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Abstract: In this paper, we prove Vojta's Main Conjecture for split blowups of products of certain elliptic curves with themselves. We then deduce from the conjecture bounds on the average number of rational points lying on curves on these surfaces, and expound upon this connection for abelian surfaces and rational surfaces.


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Additional Information

David McKinnon
Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Email: dmckinnon@math.uwaterloo.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06784-9
PII: S 0002-9939(02)06784-9
Keywords: Vojta's conjecture, heights, rational points, elliptic curves
Received by editor(s): June 22, 2001
Published electronically: August 19, 2002
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2002 American Mathematical Society