Resolution of Singularities in Arbitrary Characteristic

Abstract

Let $X$ be an integral affine or projective scheme of finite presentation over a perfect field. We prove that $X$ admits a resolution, that is, there exists a smooth scheme $\tilde{X}$ and a projective birational morphism from $\tilde{X}$ onto $X$.

141 pages. Added ell blowups. Substantially improved the structure of the method. Proofs are significantly simplified and clarified. The paper is shortened. This article supersedes the previous arXiv:2109.02968