Remarks on endomorphisms and rational points

Details Remarks on endomorphisms and rational points Remarks on endomorphisms and rational points

2010-01-07

arxiv.org/abs/1001.1150v2

Mathematics

Algebraic Geometry

LaTeX, 22 pages. v2: some minor observations added, misprints corrected, appendix modified.

Scientific paper

Let X be a variety over a number field and let f: X --> X be an "interesting" rational self-map with a fixed point q. 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 obtained by Claire Voisin and the first author in 2007).

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