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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.04271 |
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| _version_ | 1866915276143984640 |
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| author | Machida, Kai |
| author_facet | Machida, Kai |
| contents | Borger's theory of $Λ$-spaces imbues algebraic spaces, which include schemes, with an additional structure defined by an extension of the Witt vector functor. Motivated by $\mathbb{F}_1$-geometry, we prove the existence of a weak resolution of singularities in the category of $Λ$-schemes. Our arguments are based on standard arguments in characteristic $0$ using the order reduction of an ideal marked with $Λ$-equivariant data. This paper is based on work from the author's PhD thesis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04271 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Order reduction of $Λ$-marked monomial ideals and weak resolutions Machida, Kai Algebraic Geometry 14E15 Borger's theory of $Λ$-spaces imbues algebraic spaces, which include schemes, with an additional structure defined by an extension of the Witt vector functor. Motivated by $\mathbb{F}_1$-geometry, we prove the existence of a weak resolution of singularities in the category of $Λ$-schemes. Our arguments are based on standard arguments in characteristic $0$ using the order reduction of an ideal marked with $Λ$-equivariant data. This paper is based on work from the author's PhD thesis. |
| title | Order reduction of $Λ$-marked monomial ideals and weak resolutions |
| topic | Algebraic Geometry 14E15 |
| url | https://arxiv.org/abs/2505.04271 |