Forms and currents on the analytification of an algebraic variety (after Chambert-Loir and Ducros)

TL;DR

This paper surveys the recent development of real differential forms and currents on Berkovich spaces introduced by Chambert-Loir and Ducros, and compares this new theory with tropical algebraic geometry.

Contribution

It provides an overview of the theory of differential forms and currents on Berkovich spaces and relates it to tropical algebraic geometry.

Findings

Introduces a new framework for differential forms on Berkovich spaces

Connects non-Archimedean geometry with tropical geometry

Highlights similarities and differences between the theories

Abstract

Chambert-Loir and Ducros have recently introduced real differential forms and currents on Berkovich spaces. In these notes, we survey this new theory and we will compare it with tropical algebraic geometry.