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