A remark on an integral structure of the imperfect coefficient ring of $(φ,Γ)$-modules
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914497273266176 |
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| author | Watanabe, Takumi |
| author_facet | Watanabe, Takumi |
| contents | Let $K$ be a complete discrete valuation field of characteristic $0$ with perfect residue field of characteristic $p>0$. Let $\mathbb{A}_K$ denote the imperfect coefficient ring of $(φ,Γ)$-modules defined by Jean-Marc Fontaine. We prove that the canonical map $W(k_{K_\infty})[[μ]]\rightarrow \mathbb{A}_K\cap A_\mathrm{inf}$ is an isomorphism, even if $K$ is ramified. This fact was remarked by Nathalie Wach without proof. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_17559 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A remark on an integral structure of the imperfect coefficient ring of $(φ,Γ)$-modules Watanabe, Takumi Number Theory Representation Theory 11S23 Let $K$ be a complete discrete valuation field of characteristic $0$ with perfect residue field of characteristic $p>0$. Let $\mathbb{A}_K$ denote the imperfect coefficient ring of $(φ,Γ)$-modules defined by Jean-Marc Fontaine. We prove that the canonical map $W(k_{K_\infty})[[μ]]\rightarrow \mathbb{A}_K\cap A_\mathrm{inf}$ is an isomorphism, even if $K$ is ramified. This fact was remarked by Nathalie Wach without proof. |
| title | A remark on an integral structure of the imperfect coefficient ring of $(φ,Γ)$-modules |
| topic | Number Theory Representation Theory 11S23 |
| url | https://arxiv.org/abs/2604.17559 |