Periodic points, linearizing maps, and the dynamical Mordell-Lang problem

2008/05/11 by Ghioca, Dragos, Tucker, Thomas J.
#14K12 #37F10 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0805.1560

Abstract

We prove a dynamical version of the Mordell-Lang conjecture for subvarieties of quasiprojective varieties X, endowed with the action of a morphism f:X --> X. We use an analytic method based on the technique of Skolem, Mahler, and Lech, along with results of Herman and Yoccoz from nonarchimedean dynamics.

Related

• The dynamical Mordell-Lang problem for etale maps
• Mordell-Lang and Skolem-Mahler-Lech theorems for endomorphisms of semiabelian varieties
• The Dynamical Mordell-Lang Conjecture
• The Dynamical Mordell-Lang Conjecture for endomorphisms of semiabelian varieties defined over fields of positive characteristic
• The Dynamical Mordell-Lang Conjecture for skew-linear self-maps