Lectures on Local Systems in Algebraic-Arithmetic Geometry

TL;DR

This paper presents lecture notes on local systems within algebraic-arithmetic geometry, providing an overview of key concepts and recent developments in the field, based on lectures given at Columbia University in 2022.

Contribution

It compiles and elaborates on advanced topics in local systems in algebraic-arithmetic geometry, serving as an educational resource and summarizing recent progress.

Findings

Comprehensive overview of local systems in algebraic-arithmetic geometry

Connections between local systems and arithmetic properties elucidated

Framework for further research and applications established

Abstract

Those notes rest on the Samuel Eilenberg Lectures I gave at Columbia University, NY, in the fall 2022. I thank all the mathematicians who participated in their elaboration, directly or indirectly. They are meant to be published as a Springer Lecture Notes. This arXiv version is not identical with the final version.