Sufficient conditions for the dirichlet property
Huayi Chen (IMJ-PRG), Atsushi Moriwaki
TL;DR
This paper establishes sufficient conditions for the Dirichlet property of pseudoeffective adelic R-Cartier divisors using dynamical systems in Arakelov geometry, providing a numerical criterion for curves over trivially valued fields.
Contribution
It introduces new sufficient conditions and a numerical criterion for the Dirichlet property in the context of adelic R-Cartier divisors, advancing understanding in arithmetic geometry.
Findings
Sufficient conditions for the Dirichlet property are proposed.
A numerical criterion for the Dirichlet property on curves is provided.
The approach uses dynamical systems within Arakelov geometry.
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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · advanced mathematical theories · Advanced Differential Equations and Dynamical Systems