Centers of perfectoid purity

2025/04/22 by Fayolle, Anne · 1 citation
#13A35 #14B05 #14F18 #14G45 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.15569

Abstract

We introduce a mixed characteristic analog of log canonical centers in characteristic 0 and centers of F-purity in positive characteristic, which we call centers of perfectoid purity. We show that their existence detects (the failure of) normality of the ring. We also show the existence of a special center of perfectoid purity that detects the perfectoid purity of R, analogously to the splitting prime of Aberbach and Enescu, and investigate its behavior under étale morphisms.

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Cited by

• On complete integral closedness of the p-adic completion of absolute integral closure

Related

• Computation method for perfectoid purity and perfectoid BCM-regularity
• Perfectoid Spaces
• Perfectoid spaces
• Perfectoid pure singularities
• A Criterion for Perfectoid Purity and the Rationality of Thresholds