## Algebra & Number Theory

### A dynamical variant of the Pink–Zilber conjecture

#### Abstract

Let $f1,…,fn∈ℚ¯[x]$ be polynomials of degree $d>1$ such that no $fi$ is conjugate to $xd$ or to $±Cd(x)$, where $Cd(x)$ is the Chebyshev polynomial of degree $d$. We let $φ$ be their coordinatewise action on $An$, i.e., $φ:An→An$ is given by $(x1,…,xn)↦(f1(x1),…,fn(xn))$. We prove a dynamical version of the Pink–Zilber conjecture for subvarieties $V$ of $An$ with respect to the dynamical system $(An,φ)$, if $min{dim(V),codim(V)−1}≤1$.

#### Article information

Source
Algebra Number Theory, Volume 12, Number 7 (2018), 1749-1771.

Dates
Received: 1 November 2017
Revised: 6 April 2018
Accepted: 6 June 2018
First available in Project Euclid: 9 November 2018

Permanent link to this document
https://projecteuclid.org/euclid.ant/1541732440

Digital Object Identifier
doi:10.2140/ant.2018.12.1749

Mathematical Reviews number (MathSciNet)
MR3871509

Zentralblatt MATH identifier
06976301

#### Citation

Ghioca, Dragos; Nguyen, Khoa Dang. A dynamical variant of the Pink–Zilber conjecture. Algebra Number Theory 12 (2018), no. 7, 1749--1771. doi:10.2140/ant.2018.12.1749. https://projecteuclid.org/euclid.ant/1541732440

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