The canonical heights for Jordan blocks of small eigenvalues, preperiodic points, and the arithmetic degrees

Abstract

We introduce a new canonical height function for Jordan blocks of small eigenvalues for endomorphisms on smooth projective varieties over a number field. We prove that under an assumption on the eigenvalues of the endomorphism on the group of divisors modulo numerical equivalence, the arithmetic degree at a rational point is equal to one if and only if it is preperiodic under the endomorphism.

arXiv comment18 pages

References in corpus (1)

• On upper bounds of arithmetic degrees

Cited by in corpus (5)

• Non-density of points of small arithmetic degrees
• Invariant subvarieties with small dynamical degree
• Kawaguchi-Silverman conjecture for endomorphisms on several classes of varieties
• Arithmetic and dynamical degrees of self-morphisms of semi-abelian varieties
• Effective Eigendivisors and the Kawaguchi-Silverman Conjecture