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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.24926 |
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| _version_ | 1866914422780329984 |
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| author | Takamatsu, Teppei Yoshikawa, Shou |
| author_facet | Takamatsu, Teppei Yoshikawa, Shou |
| contents | We study the perfectoid pure threshold with respect to $p$, an invariant of singularities in mixed characteristic $(0,p)$ arising from perfectoid purity. In this paper, we compute perfectoid pure thresholds for lifts of rational double points. We show that the set of such thresholds is contained in $\mathbb{Q}$ and satisfies the ascending chain condition. In characteristic $2$, all reciprocals of positive integers occur, and $0$ is the unique accumulation point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24926 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Perfectoid pure thresholds of lifts of rational double points Takamatsu, Teppei Yoshikawa, Shou Algebraic Geometry We study the perfectoid pure threshold with respect to $p$, an invariant of singularities in mixed characteristic $(0,p)$ arising from perfectoid purity. In this paper, we compute perfectoid pure thresholds for lifts of rational double points. We show that the set of such thresholds is contained in $\mathbb{Q}$ and satisfies the ascending chain condition. In characteristic $2$, all reciprocals of positive integers occur, and $0$ is the unique accumulation point. |
| title | Perfectoid pure thresholds of lifts of rational double points |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2603.24926 |