Sufficient conditions for the dirichlet property

Abstract

The effectivity up to R-linear equivalence (Dirichlet property) of pseudoeffective adelic R-Cartier divisors is a subtle problem in arithmetic geometry. In this article, we propose sufficient conditions for the Dirichlet property by using the dynamic system in the classic Arakelov geometry setting. We also give a numerical criterion of the Dirichlet property for adelic R-Cartier divisors on curves over a trivially valued field.

References in corpus (1)

• Toward Dirichlet's unit theorem on arithmetic varieties

Cited by in corpus (2)

• Volume function over a trivially valued field
• Hyperbolic polarized dynamics, pairs of inverse maps and the Dirichlet property