Remarks on endomorphisms and rational points

E. Amerik, F. Bogomolov, M. Rovinsky

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)1819-1842
Number of pages24
JournalCompositio Mathematica
Issue number6
StatePublished - Nov 2011


  • p-adic neighbourhood
  • rational maps
  • rational points

ASJC Scopus subject areas

  • Algebra and Number Theory


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