Dynamical Mordell-Lang conjecture for split self-maps of affine curve times projective curve

TL;DR

This paper proves the dynamical Mordell-Lang conjecture for products of endomorphisms on affine and projective curves over algebraic numbers, advancing understanding in arithmetic dynamics.

Contribution

It establishes the conjecture for split self-maps on affine curve times projective curve, a case previously unresolved.

Findings

Proves the conjecture for affine and projective curve products over algebraic numbers.

Extends the scope of dynamical Mordell-Lang conjecture to new classes of maps.

Provides new techniques for analyzing endomorphisms on algebraic curves.

Abstract

We prove the dynamical Mordell-Lang conjecture for product of endomorphisms of an affine curve and a projective curve over $\overline{\mathbb{Q}}$.