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arXiv · 1312.3528

Algebraic dynamical systems and Dirichlet's unit theorem on arithmetic varieties

Huayi Chen·Atsushi Moriwaki
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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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Huayi Chen, Atsushi Moriwaki. 2013-12-12. Algebraic dynamical systems and Dirichlet's unit theorem on arithmetic varieties. https://arxiv.org/abs/1312.3528

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