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arXiv · 2504.02966

On deformation of perfectoid purity in Gorenstein domains

Benjamin Baily·Karina Dovgodko·Austyn Simpson·Jack Westbrook
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Abstract

If $(R,\mathfrak{m})$ is a complete local ring of mixed characteristic $(0,p)$ and $R/pR$ is an $F$-pure Gorenstein domain, we find a sufficient condition for $R$ to be perfectoid pure. This condition is related to the Cohen-Macaulayness of the absolute integral closures of Gorenstein local domains of mixed characteristic which are not necessarily excellent. Along the way, we show that the problem of lifting $F$-purity of $R/pR$ to perfectoid purity of $R$ is equivalent to a similar deformation problem for the splinter property.

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Benjamin Baily, Karina Dovgodko, Austyn Simpson, Jack Westbrook. 2025-04-03. On deformation of perfectoid purity in Gorenstein domains. https://arxiv.org/abs/2504.02966

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