The Dynamical Mordell Lang Conjecture For Polynomial Endomorphisms Of The Affine Plane
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The Dynamical Mordell-Lang Conjecture for Polynomial Endomorphisms of the Affine Plane
In this paper we prove the Dynamical Mordell-Lang Conjecture for polynomial endomorphisms of the affine plane over the algebraic numbers. More precisely, let f be an endomorphism of the affine plan over the algebraic numbers. Let x be a point in the affine plan and C be a curve. If the intersection of C and the orbits of x is infinite, then C is periodic.
The Dynamical Mordell–Lang Conjecture
Author: Jason P. Bell
language: en
Publisher: American Mathematical Soc.
Release Date: 2016-04-20
The Dynamical Mordell-Lang Conjecture is an analogue of the classical Mordell-Lang conjecture in the context of arithmetic dynamics. It predicts the behavior of the orbit of a point x under the action of an endomorphism f of a quasiprojective complex variety X. More precisely, it claims that for any point x in X and any subvariety V of X, the set of indices n such that the n-th iterate of x under f lies in V is a finite union of arithmetic progressions. In this book the authors present all known results about the Dynamical Mordell-Lang Conjecture, focusing mainly on a p-adic approach which provides a parametrization of the orbit of a point under an endomorphism of a variety.
A Torsion Jacquet-Langlands Correspondence
"We prove a numerical form of a Jacquet-Langlands correspondence for torsion classes on arithmetic hyperbolic 3-manifolds." -- Prové de l'editor.