On the Arithmetic Dynamics of Monomial Maps

Abstract

We generalized several results for the arithmetic dynamics of monomial maps, including Silverman's conjectures on height growth, dynamical Mordell-Lang conjecture, and dynamical Manin-Mumford conjecture. These results are originally known for monomial maps on algebraic tori. We extend the results to arbitrary toric varieties.

References in corpus (2)

• The dynamical Mordell-Lang problem for etale maps
• The Dynamical Manin-Mumford Conjecture and the Dynamical Bogomolov Conjecture for split rational maps

Cited by in corpus (3)

• Kawaguchi-Silverman conjecture for endomorphisms on rationally connected varieties admitting an int-amplified endomorphism
• Kawaguchi-Silverman conjecture for endomorphisms on several classes of varieties
• Arithmetic and dynamical degrees of self-morphisms of semi-abelian varieties