On the $(φ,Γ)$-modules corresponding to crystalline representations
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914493378854912 |
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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 $p>0$. We introduce the notion of crystalline $(φ,Γ)$-modules over $\widetilde{\mathbb{A}}_K^{+}$ and show that their category is equivalent to the category of crystalline $\mathbb{Z}_p$-representations of the absolute Galois group of $K$. In other words, we determine the $(φ,Γ)$-modules over $\widetilde{\mathbb{A}}_K$ that correspond to crystalline representations. This equivalence generalizes, in certain respects, that of L. Berger in the unramified case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19829 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the $(φ,Γ)$-modules corresponding to crystalline representations Watanabe, Takumi Number Theory Representation Theory 11S23 Let $K$ be a complete discrete valuation field of characteristic $0$ with perfect residue field of characteristic $p>0$. We introduce the notion of crystalline $(φ,Γ)$-modules over $\widetilde{\mathbb{A}}_K^{+}$ and show that their category is equivalent to the category of crystalline $\mathbb{Z}_p$-representations of the absolute Galois group of $K$. In other words, we determine the $(φ,Γ)$-modules over $\widetilde{\mathbb{A}}_K$ that correspond to crystalline representations. This equivalence generalizes, in certain respects, that of L. Berger in the unramified case. |
| title | On the $(φ,Γ)$-modules corresponding to crystalline representations |
| topic | Number Theory Representation Theory 11S23 |
| url | https://arxiv.org/abs/2405.19829 |