A Dynamical Variant of the Pink-zilber Conjecture


Let f1, . . . , fn ∈ Q[x] be polynomials of degree d > 1 such that no fi is conjugated to x d or to ±Cd(x), where Cd(x) is the Chebyshev polynomial of degree d. We let φ be their coordinatewise action on A, i.e., φ : A −→ A is given by (x1, . . . , xn) 7→ (f1(x1), . . . , fn(xn)). We prove a dynamical version of the Pink-Zilber conjecture for subvarieties V of A with respect to the dynamical system (A, φ), if min{dim(V ), codim(V )− 1} ≤ 1.

Cite this paper

@inproceedings{Nguyen2017ADV, title={A Dynamical Variant of the Pink-zilber Conjecture}, author={Ken D. Nguyen}, year={2017} }