Absolute desingularization in characteristic zero

TL;DR

This paper surveys recent advances in the resolution of singularities for quasi-excellent schemes in characteristic zero, emphasizing examples and main ideas rather than technical details.

Contribution

It provides an accessible overview of the latest progress in absolute desingularization techniques in characteristic zero, highlighting key concepts and developments.

Findings

Summarizes recent progress in desingularization of schemes

Provides illustrative examples and main ideas

References detailed proofs and technical sources

Abstract

We present a survey on the recent progress with desingularization of quasi-excellent schemes of characteristic zero. Due to expository goals of the paper we concentrate on giving examples and outlining main ideas, and we refer to other sources for detailed proofs and technical details. This survey will be published in the proceedings of the conference "Motivic integration and its interactions with model theory and non-archimedean geometry" (ICMS, May 2008).