A Kunz-type characterization of regular rings via alterations

2018/10/18 by Ma, Linquan, Schwede, Karl · 1 citation
#13A35 #13D05 #13D45 #14B05 #14B15 #14F17 #14F18 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1810.08172

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 π: X → Spec R, we have that R π_* O_X has finite (equivalently zero in characteristic zero) projective dimension.

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• The Briançon-Skoda theorem for pseudo-rational and Du Bois singularities and uniformity in excellent rings

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