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2022 Zariski Density of Points with Maximal Arithmetic Degree
Kaoru Sano, Takahiro Shibata
Michigan Math. J. Advance Publication 1-20 (2022). DOI: 10.1307/mmj/20205960

Abstract

Given a dominant rational self-map on a projective variety over a number field, we can define the arithmetic degree at a rational point. It is known that the arithmetic degree at any point is less than or equal to the first dynamical degree. In this paper, we show that there are densely many Q-rational points with maximal arithmetic degree (i.e., whose arithmetic degree is equal to the first dynamical degree) for self-morphisms on projective varieties. For unirational varieties and Abelian varieties, we show that there are densely many rational points with maximal arithmetic degree over a sufficiently large number field. We also give a generalization of a result of Kawaguchi and Silverman in the Appendix.

Citation

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Kaoru Sano. Takahiro Shibata. "Zariski Density of Points with Maximal Arithmetic Degree." Michigan Math. J. Advance Publication 1 - 20, 2022. https://doi.org/10.1307/mmj/20205960

Information

Received: 3 August 2020; Revised: 6 December 2020; Published: 2022
First available in Project Euclid: 29 April 2022

Digital Object Identifier: 10.1307/mmj/20205960

Subjects:
Primary: 37P55
Secondary: 14G05

Rights: Copyright © 2022 The University of Michigan

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