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arXiv · 2604.27270

Perfectoid splitting and global $+$-regularity for smooth hypersurfaces

Shou Yoshikawa
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Abstract

In this paper, we prove that smooth Calabi--Yau hypersurfaces of degree $d$ over complete unramified discrete valuation rings with residue characteristic $p$ are perfectoid split if $p$ is larger than the relative dimension and $p\nmid d$. We also show that unramified lifts of smooth Fano hypersurfaces over fields of characteristic $p>0$ are globally $+$-regular if $p\ge \dim X$ and $p\nmid d$.

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Shou Yoshikawa. 2026-04-29. Perfectoid splitting and global $+$-regularity for smooth hypersurfaces. https://arxiv.org/abs/2604.27270

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