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.
´Etale fundamental groups of Kawa- mata log terminal spaces, flat sheaves, and quotients of abelian varieties
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Dynamical Iitaka theory on Fano contractions
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.