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

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.

36 pages

References in corpus (3)

• Toward Dirichlet's unit theorem on arithmetic varieties
• Toward a geometric analogue of Dirichlet's unit theorem
• Adelic divisors on arithmetic varieties