Formal and rigid geometry: an intuitive introduction, and some applications

TL;DR

This paper provides an accessible overview of formal and rigid geometry over complete discrete valuation rings, highlighting recent applications in algebraic geometry, arithmetic geometry, and singularity theory, including Milnor fibrations and motivic zeta functions.

Contribution

It offers an intuitive introduction to formal and rigid geometry and discusses recent significant applications in algebraic and arithmetic geometry.

Findings

Application to Milnor fibration

Insights into motivic zeta functions

Connections between geometry and singularity theory

Abstract

We give an informal introduction to formal and rigid geometry over complete discrete valuation rings, and we discuss some applications in algebraic and arithmetic geometry and singularity theory, with special emphasis on recent applications to the Milnor fibration and the motivic zeta function by J. Sebag and the author.