Remarks on endomorphisms and rational points

DOI10.1112/S0010437X11005537zbMath1231.14014arXiv1001.1150OpenAlexW2111456832MaRDI QIDQ3107319

Ekaterina Amerik, M. Z. Rovinskij, Fedor A. Bogomolov

Publication date: 23 December 2011

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.1150

zbMATH Keywords

rational points on algebraic varietiesrational endomorphisms

Mathematics Subject Classification ID

Rational points (14G05) Non-Archimedean dynamical systems (11S82) Arithmetic dynamics on general algebraic varieties (37P55)

Related Items (10)

Integral points and orbits of endomorphisms on the projective plane ⋮ Linear relations between polynomial orbits ⋮ Remarks on algebraic dynamics in positive characteristic ⋮ Invariant varieties for polynomial dynamical systems ⋮ Examples of dynamical degree equals arithmetic degree ⋮ Density of orbits of dominant regular self-maps of semiabelian varieties ⋮ The existence of Zariski dense orbits for polynomial endomorphisms of the affine plane ⋮ Density of orbits of endomorphisms of abelian varieties ⋮ Current trends and open problems in arithmetic dynamics ⋮ Potential density of projective varieties having an int-amplified endomorphism

Cites Work

• Meromorphic fibrations on certain manifolds with trivial canonical bundle
• Potential density of rational points on the variety of lines of a cubic fourfold
• \(K3\) surfaces with Picard number one and infinitely many rational points
• Periodic points, linearizing maps, and the dynamical Mordell-Lang problem
• Complete intersections with middle Picard number 1 defined over \({\mathbb{Q}}\)
• Hypersurfaces solutions d'une équation de Pfaff analytique
• Orbifolds, special varieties and classification theory.
• A computation of invariants of a rational self-map
• The intermediate Jacobian of the cubic threefold
• Rational curves on general projective hypersurfaces
• Density of rational points on elliptic \(K3\) surfaces
• A correction: ``On a conjecture of Clemens on rational curves on hypersurfaces

This page was built for publication: Remarks on endomorphisms and rational points