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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2308.11191 |
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| _version_ | 1866908684846628864 |
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| author | Abhinandan |
| author_facet | Abhinandan |
| contents | For an absolutely unramified field extension $L/\mathbb{Q}_p$ with imperfect residue field, we define and study Wach modules in the setting of $(φ,Γ)$-modules for $L$. Our main result establishes a direct equivalence between the category of lattices inside crystalline representations of the absolute Galois group of $L$ and the category of integral Wach modules for $L$. Moreover, we provide a direct relation between a rational Wach module equipped with the Nygaard filtration and the filtered $φ$-module of its associated crystalline representation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_11191 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Crystalline representations and Wach modules in the imperfect residue field case Abhinandan Number Theory 14F20, 14F30, 14F40, 11S23 For an absolutely unramified field extension $L/\mathbb{Q}_p$ with imperfect residue field, we define and study Wach modules in the setting of $(φ,Γ)$-modules for $L$. Our main result establishes a direct equivalence between the category of lattices inside crystalline representations of the absolute Galois group of $L$ and the category of integral Wach modules for $L$. Moreover, we provide a direct relation between a rational Wach module equipped with the Nygaard filtration and the filtered $φ$-module of its associated crystalline representation. |
| title | Crystalline representations and Wach modules in the imperfect residue field case |
| topic | Number Theory 14F20, 14F30, 14F40, 11S23 |
| url | https://arxiv.org/abs/2308.11191 |