Remarks on endomorphisms and rational points
Algebraic Geometry
2019-02-20 v2
Abstract
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).
Cite
@article{arxiv.1001.1150,
title = {Remarks on endomorphisms and rational points},
author = {Ekaterina Amerik and Fedor Bogomolov and Marat Rovinsky},
journal= {arXiv preprint arXiv:1001.1150},
year = {2019}
}
Comments
LaTeX, 22 pages. v2: some minor observations added, misprints corrected, appendix modified.