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

Kaoru Sano

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arXiv · 1712.07533

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

Kaoru Sano

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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.

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Kaoru Sano. 2017-12-20. The canonical heights for Jordan blocks of small eigenvalues, preperiodic points, and the arithmetic degrees. https://arxiv.org/abs/1712.07533

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