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Remarks on endomorphisms and rational points
Part of:
Algebraic number theory: local and $p$-adic fields
Arithmetic problems. Diophantine geometry
Arithmetic and non-Archimedean dynamical systems
Published online by Cambridge University Press: 24 August 2011
Abstract
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Let X be an algebraic variety and let f:X−−→X be a rational self-map with a fixed point q, where everything is defined over a number field K. We make some general remarks concerning the possibility of using the behaviour of f near q to produce many rational points on X. As an application, we give a simplified proof of the potential density of rational points on the variety of lines of a cubic fourfold, originally proved by Claire Voisin and the first author in 2007.
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- Copyright © Foundation Compositio Mathematica 2011
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