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arXiv · 2610.32577

Noetherian local rings without perfectoid towers

Tatsuki Yamaguchi
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Abstract

Let $k$ be a perfect field of characteristic $p>0$. We prove that if a $p$-torsionfree ring $R$, defined by homogeneous equations over $W(k)$, admits a perfectoid tower arising from $(R,(p))$, then its special fiber is $F$-liftable. We also give explicit examples admitting no such tower, including examples with $F$-liftable special fibers.

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Tatsuki Yamaguchi. 2026-10-23. Noetherian local rings without perfectoid towers. https://arxiv.org/abs/2610.32577

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