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The canonical heights for Jordan blocks of small eigenvalues, preperiodic points, and the arithmetic degrees (1712.07533v1)
Published 20 Dec 2017 in math.AG, math.DS, and math.NT
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.
