September 16, 2025Open Access

Centers of perfectoid purity

Key Points

Centers of perfectoid purity can reveal the non-normality of rings, which is crucial in algebraic geometry.
A special center of perfectoid purity can signal the perfectoid purity of rings, providing valuable insights.
The investigation includes the behavior of these centers under étale morphisms, expanding the understanding of their properties.
These findings create parallels with existing concepts like log canonical centers, enhancing existing algebraic frameworks.

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 the ring, analogously to the splitting prime of Aberbach and Enescu, and investigate its behavior under étale morphisms.

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Cite This Study

Anne Fayolle (Mon,) studied this question.

synapsesocial.com/papers/68d454c531b076d99fa59fa1 https://doi.org/https://doi.org/10.5802/jep.313

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