The canonical heights for Jordan blocks of small eigenvalues, preperiodic points, and the arithmetic degrees
Algebraic Geometry
2017-12-21 v1 Dynamical Systems
Number Theory
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.
Keywords
Cite
@article{arxiv.1712.07533,
title = {The canonical heights for Jordan blocks of small eigenvalues, preperiodic points, and the arithmetic degrees},
author = {Kaoru Sano},
journal= {arXiv preprint arXiv:1712.07533},
year = {2017}
}
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18 pages