$δ$-lifting and $1$-dimensional analytic fields
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866917122382233600 |
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| author | Yu, Jiahong |
| author_facet | Yu, Jiahong |
| contents | Let $k$ be an algebraically closed complete non-Archimedean field, and let $K$ be a finitely generated field extension over $k$ with transcendence degree $1$. Equip $K$ a non-Archimedean norm extending the one on $k$, and let $\mathcal{K}$ denote the completion of $K$. We will prove that the valuation ring $\mathcal{K}^+$ admits a flat $δ$-lifting over $\mathbb{A}_{\mathrm{inf}}(k^+)$ if and only if $\mathcal{K}$ is not of type 4. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03952 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $δ$-lifting and $1$-dimensional analytic fields Yu, Jiahong Commutative Algebra Let $k$ be an algebraically closed complete non-Archimedean field, and let $K$ be a finitely generated field extension over $k$ with transcendence degree $1$. Equip $K$ a non-Archimedean norm extending the one on $k$, and let $\mathcal{K}$ denote the completion of $K$. We will prove that the valuation ring $\mathcal{K}^+$ admits a flat $δ$-lifting over $\mathbb{A}_{\mathrm{inf}}(k^+)$ if and only if $\mathcal{K}$ is not of type 4. |
| title | $δ$-lifting and $1$-dimensional analytic fields |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2512.03952 |