Heights and measures on analytic spaces. A survey of recent results, and some remarks

TL;DR

This survey reviews recent developments in constructing measures on non-archimedean analytic spaces linked to metrized line bundles, highlighting applications, examples, and related results in the field.

Contribution

The paper introduces a novel construction of measures on non-archimedean analytic varieties associated with metrized line bundles and discusses its applications and related results.

Findings

New measure construction on non-archimedean analytic spaces

Applications to metrized line bundles and related areas

Enhanced understanding of measures in non-archimedean geometry

Abstract

This paper has two goals. The first is to present the construction, due to the author, of measures on non-archimedean analytic varieties associated to metrized line bundles and some of its applications. We take this opportunity to add remarks, examples and mention related results.