Topics in Adic Spaces

TL;DR

This paper provides an overview of adic spaces, covering their properties, connections to formal geometry, and relations to Berkovich spaces, based on a series of lectures at a non-archimedean geometry school.

Contribution

It offers a comprehensive exposition of adic spaces, highlighting their key features and links to other non-archimedean geometric frameworks, based on recent lecture notes.

Findings

Detailed discussion of coherent sheaves on adic spaces

Analysis of morphism properties in adic spaces

Connections between adic spaces, formal geometry, and Berkovich spaces

Abstract

These are expanded notes from a four lecture mini-course given by the author at the Spring School on Non-archimedean geometry and Eigenvarieties, held at the University of Heidelberg in March 2023. The course discusses coherent sheaves, various properties of morphisms, as well as the links to formal geometry and Berkovich spaces.