On the Arithmetic Dynamics of Monomial Maps

Jan-Li Lin

On the Arithmetic Dynamics of Monomial Maps

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arxiv 1704.02661 v1 pith:CBSQI445 submitted 2017-04-09 math.DS math.AGmath.NT

Jan-Li Lin This is my paper · ORCID

classification math.DSmath.AGmath.NT

keywords mapsmonomialresultsarithmeticconjecturedynamicaldynamicsalgebraic

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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.

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Kawaguchi-Silverman conjecture for endomorphisms on rationally connected varieties admitting an int-amplified endomorphism
math.AG 2019-08 conditional novelty 7.0 of 10

Every surjective self-map of a smooth rationally connected projective variety with an int-amplified endomorphism satisfies the Kawaguchi-Silverman conjecture.

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