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

Huayi Chen, Atsushi Moriwaki

Published 2013-12-12, updated 2014-02-22Version 4

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.