Quasi-Gorenstein (Normal) Finite Covers in Arbitrary Characteristic

TL;DR

This paper proves that any complete local normal domain and any normal projective variety over a field can be extended or covered by a quasi-Gorenstein domain or variety, resolving cases in characteristic two.

Contribution

It establishes the existence of finite quasi-Gorenstein extensions for normal domains and covers for normal projective varieties in arbitrary characteristic, including characteristic two.

Findings

Existence of module-finite quasi-Gorenstein extensions for normal domains.

Existence of finite surjective morphisms from quasi-Gorenstein varieties to given varieties.

Resolution of the open case for residual characteristic two.

Abstract

We show that any complete local (normal) domain admits a module-finite quasi-Gorenstein normal (complete local) domain extension. In the geometric vein, we show that any normal projective variety $X$ over a field admits a finite surjective morphism $Y\rightarrow X$ from a normal quasi-Gorenstein projective variety $Y$. Notably, our results resolve the previously open case for residual characteristic two.