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Ph.D. Thesis on Characteristic Currents on Berkovich Spaces
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Jakob Werner 23382e6fb9 fix: typo 
Thanks to Johannes Witzig for spotting and reporting
2025年09月20日 11:45:04 +02:00
contents fix: typo 2025年09月20日 11:45:04 +02:00
preamble Fixed Typo and removed unnecessary macro 2024年02月10日 11:51:26 +01:00
references Typo 2023年11月25日 17:23:03 +01:00
.gitignore Don't track .pdf 2023年05月03日 13:12:36 +02:00
.latexmkrc Added .latexmkrc 2023年03月29日 17:41:51 +02:00
README.md doc: updated readme 2025年09月20日 11:43:22 +02:00
thesis.tex cleaned up visuals and title page 2024年02月09日 12:34:58 +01:00

Characteristic Currents for Metrized Vector Bundles on Berkovich Spaces

This repository contains the LaTeX sources for my Ph.D. thesis called Characteristic Currents for Metrized Vector Bundles on Berkovich Spaces which I completed under the supervision of Prof. Klaus Künnemann in November 2023.

Abstract

We define and study Segre and Chern currents for locally approachably (pseudo-)metrized vector bundles on Berkovich spaces, generalizing the first Chern currents of metrized line bundles introduced by Chambert-Loir and Ducros. By the Poincaré-Lelong formula they give rise to classes in Bott-Chern cohomology which do not depend on the metric, and which we compare to classes constructed by means of Liu's tropical cycle class map. In top degree, products of Segre and Chern currents are even signed Radon measures, generalizing Monge-Ampère measures of metrized line bundles first introduced by Chambert-Loir.

Build

With a modern TeX distribution, the sources can be compiled by running

latexmk

inside the project directory.