Perfectoid splitting and global $+$-regularity for smooth hypersurfaces
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866909003322228736 |
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| author | Yoshikawa, Shou |
| author_facet | Yoshikawa, Shou |
| contents | 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 $p\nmid d$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27270 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Perfectoid splitting and global $+$-regularity for smooth hypersurfaces Yoshikawa, Shou Algebraic Geometry 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 $p\nmid d$. |
| title | Perfectoid splitting and global $+$-regularity for smooth hypersurfaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2604.27270 |