Algebraic dynamical systems and Dirichlet's unit theorem on arithmetic varieties
Algebraic Geometry
2014-02-25 v4
Abstract
In this paper, we study obstructions to the Dirichlet property by two approaches: density of non-positive points and functionals on adelic R-divisors. Applied to the algebraic dynamical systems, these results provide examples of nef adelic arithmetic R-Cartier divisor which does not have the Dirichlet property. We hope the obstructions obtained in the article will give ways toward criteria of the Dirichlet property.
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Cite
@article{arxiv.1312.3528,
title = {Algebraic dynamical systems and Dirichlet's unit theorem on arithmetic varieties},
author = {Huayi Chen and Atsushi Moriwaki},
journal= {arXiv preprint arXiv:1312.3528},
year = {2014}
}
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36 pages