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arXiv · 2502.06108

Computation method for perfectoid purity and perfectoid BCM-regularity

Shou Yoshikawa
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Abstract

In this paper, we introduce the notion of quasi-$F$-splitting for rings in mixed characteristic. By comparing quasi-$F$-splitting with perfectoid purity, we obtain a new inversion of adjunction-type result. Furthermore, we study the possible values of the perfectoid pure threshold of $\mathrm{div}(p)$ and construct new examples of perfectoid pure rings.

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Shou Yoshikawa. 2025-02-10. Computation method for perfectoid purity and perfectoid BCM-regularity. https://arxiv.org/abs/2502.06108

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