A Kunz-type characterization of regular rings via alterations
classification
🧮 math.AC
math.AG
keywords
regularfinitezeroalterationalterationscharacteristiccharacterizationdimension
read the original 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 $\pi : X \to Spec R$, we have that $R \pi_* \mathcal{O}_X$ has finite (equivalently zero in characteristic zero) projective dimension.
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