Resolution of Singularities in Arbitrary Characteristic

TL;DR

This paper proves that any integral scheme of finite presentation over a perfect field admits a resolution of singularities, resulting in a smooth scheme via a projective birational morphism.

Contribution

It establishes the existence of resolutions of singularities for schemes over perfect fields in arbitrary characteristic, extending previous results.

Findings

Existence of smooth resolutions for integral schemes over perfect fields.

Construction of a projective birational morphism from the resolution.

Applicable to schemes of finite presentation over perfect fields.

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 $\widetilde X$ and a projective birational morphism from $\widetilde X$ onto $X$.