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International Mathematics Research Notices Advance Access published online on March 5, 2009
International Mathematics Research Notices, doi:10.1093/imrn/rnp022
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© The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org.

Rational Points of Definable Sets and Results of André–Oort–Manin–Mumford type

Jonathan Pila

School of Mathematics, University of Bristol, Bristol BS8 1TW, UK

Correspondence: Correspondence to be sent to: j.pila{at}bristol.ac.uk

We prove some simple special cases, partly new, of results of André–Oort–Manin–Mumford type using an extension to algebraic points of bounded degree of a result of Pila–Wilkie on the density of rational points on sets definable in an o-minimal structure. The strategy follows that of a recent new proof of the Manin–Mumford conjecture by Pila–Zannier, and a proof of a special (but new) case of Pink's relative Manin–Mumford conjecture by Masser–Zannier.


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