Remarks on endomorphisms and rational points

E. Amerik, Fedor Bogomolov, M. Rovinsky

Research output: Contribution to journalArticle

Abstract

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
Volume147
Issue number6
DOIs
StatePublished - Nov 2011

Fingerprint

Rational Points
Endomorphisms
Algebraic Variety
Number field
Fixed point
Line

Keywords

  • p-adic neighbourhood
  • rational maps
  • rational points

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Remarks on endomorphisms and rational points. / Amerik, E.; Bogomolov, Fedor; Rovinsky, M.

In: Compositio Mathematica, Vol. 147, No. 6, 11.2011, p. 1819-1842.

Research output: Contribution to journalArticle

Amerik, E. ; Bogomolov, Fedor ; Rovinsky, M. / Remarks on endomorphisms and rational points. In: Compositio Mathematica. 2011 ; Vol. 147, No. 6. pp. 1819-1842.
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