Recent advances on Kawaguchi-Silverman conjecture

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Yohsuke Matsuzawa This is my paper · ORCID

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keywords conjecturekawaguchi-silvermanadvancesrecentsurvey

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This is a survey on Kawaguchi-Silverman conjecture.

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Arithmetic Degrees are Cohomological Lyapunov Multipliers
math.DS 2025-07 conditional novelty 7.0 of 10

For surjective endomorphisms of normal projective varieties over characteristic zero fields, the arithmetic degree of any Zariski dense orbit must be a cohomological Lyapunov multiplier; if the first dynamical degree ...
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math.AG 2025-07 accept novelty 7.0 of 10

For a dominant rational self-map on a projective variety, the height associated with a closed subscheme vanishes relative to an ample height along generic orbits whenever a dynamical degree is strictly smaller than th...
Dynamical Iitaka theory on Fano contractions
math.AG 2025-06 conditional novelty 7.0 of 10

The Kawaguchi-Silverman conjecture is proved for projective bundles over abelian varieties or smooth projective varieties of Picard number one, via new structure theorems for endomorphisms of Fano contractions.