Rational Points of Definable Sets and Results of Andre-Oort-Manin-Mumford type

Rational Points of Definable Sets and Results of Andre-Oort-Manin-Mumford type

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 pro...

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Príomhchruthaitheoir: Pila, J
Formáid: Journal article
Teanga:English
Foilsithe / Cruthaithe: 2009
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Achoimre: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 relativeManin-Mumford conjecture by Masser-Zannier. © 2009 The Author. Published by Oxford University Press. All rights reserved.

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