A Kunz-type characterization of regular rings via alterations

Abstract

We prove that a local domain $R$, essentially of finite type over a field, is regular if and only if for every regular alteration $\pi :X\to SpecR$, we have that $R{\pi }_{\ast }{\mathcal{O}}_X$ has finite (equivalently zero in characteristic zero) projective dimension.

7 pages, minor changes and clarifications of the explanations