Functorial stratifications of singularities in characteristic 0

Abstract

We prove that the riso-stratifications of singularities of affine algebraic sets introduced by Bradley-Williams--Halupczok are embedding independent and can be computed étale locally. Building on this, we upgrade their procedure, originally formulated in non-archimedean and model-theoretic language, into a sharp canonical and functorial stratification process for schemes of finite type over fields of characteristic 0. Our work enables comparisons with classical approaches to singularities and makes these stratifications available without requiring familiarity with the original methods.