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arXiv · 2504.15569

Centers of perfectoid purity

Anne Fayolle
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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 \'etale morphisms.

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Anne Fayolle. 2025-04-22. Centers of perfectoid purity. https://doi.org/10.5802/jep.313

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