Global pluripotential theory over a trivially valued field

TL;DR

This paper extends global pluripotential theory to Berkovich spaces over trivially valued fields, introducing new tools for analyzing functions, measures, and the Monge-Ampère operator in non-Archimedean geometry.

Contribution

It develops a comprehensive framework for pluripotential theory over trivially valued fields, including definitions of finite energy functions and measures, and studies the valuation space topology.

Findings

Defined non-Archimedean Monge-Ampère operator on projective varieties

Analyzed the topology of valuation spaces of linear growth

Explored the behavior of psh functions in this setting

Abstract

We develop global pluripotential theory in the setting of Berkovich geometry over a trivially valued field. Specifically, we define and study functions and measures of finite energy and the non-Archimedean Monge-Ampere operator on any (possibly reducible) projective variety. We also investigate the topology of the space of valuations of linear growth, and the behavior of psh functions thereon.