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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2501.13580 |
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| _version_ | 1866913800704229376 |
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| author | Du, Changjiang |
| author_facet | Du, Changjiang |
| contents | Let $K$ be an unramified extension of $\mathbb{Q}_p$, and $E$ a finite extension of $K$ with ring of integers $\mathcal{O}_E$. We associate to every finite type continuous $\mathcal{O}_E$-representation $ρ$ of $\mathrm{Gal}(\overline{K}/K)$ an étale $(φ_q,\mathcal{O}_K^{\times})$-module $D_{A_{\mathrm{mv},E}}^{(0)}(ρ)$ over $A_{\mathrm{mv},E}$, where $A_{\mathrm{mv},E}$ is the $p$-adic completion of a completed localization of the Iwasawa algebra $\mathcal{O}_E[\negthinspace[\mathcal{O}_K]\negthinspace]$. Furthermore, we prove that the functor $D_{A_{\mathrm{mv},E}}^{(0)}$ is fully faithful and exact. This functor is a $p$-adic analogue of $D_A^{(0)}$ in the recent work of Breuil, Herzig, Hu, Morra and Schraen. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_13580 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multivariable $(φ_q,\mathcal{O}_K^{\times})$-modules associated to $p$-adic representations of $\mathrm{Gal}(\overline{K}/K)$ Du, Changjiang Number Theory Let $K$ be an unramified extension of $\mathbb{Q}_p$, and $E$ a finite extension of $K$ with ring of integers $\mathcal{O}_E$. We associate to every finite type continuous $\mathcal{O}_E$-representation $ρ$ of $\mathrm{Gal}(\overline{K}/K)$ an étale $(φ_q,\mathcal{O}_K^{\times})$-module $D_{A_{\mathrm{mv},E}}^{(0)}(ρ)$ over $A_{\mathrm{mv},E}$, where $A_{\mathrm{mv},E}$ is the $p$-adic completion of a completed localization of the Iwasawa algebra $\mathcal{O}_E[\negthinspace[\mathcal{O}_K]\negthinspace]$. Furthermore, we prove that the functor $D_{A_{\mathrm{mv},E}}^{(0)}$ is fully faithful and exact. This functor is a $p$-adic analogue of $D_A^{(0)}$ in the recent work of Breuil, Herzig, Hu, Morra and Schraen. |
| title | Multivariable $(φ_q,\mathcal{O}_K^{\times})$-modules associated to $p$-adic representations of $\mathrm{Gal}(\overline{K}/K)$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2501.13580 |