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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2410.09475 |
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| _version_ | 1866909925839470592 |
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| author | Marquis, Nataniel |
| author_facet | Marquis, Nataniel |
| contents | Let $Δ$ be a finite set. We adapt the techniques of Carter-Kedlaya-Zábrádi to obtain a multivariable Fontaine equivalence which relates continuous finite dimensional $\mathbb{F}_q$-representations of $\prod_{α\in Δ} \mathcal{G}_{\mathbb{F}_q(\!(X)\!)}$ to multivariable $φ$-modules over a $\mathbb{F}_q$-algebra which is a domain. From this, we deduce a multivariable Lubin-Tate Fontaine equivalence for continuous finite type $\mathcal{O}_K$-representations of $\prod_{α\in Δ} \mathcal{G}_K$, where $K|\mathbb{Q}_p$ is a finite extension. We also obtain a plectic Fontaine equivalence and two equivalences for the subgroup $\mathcal{G}_{K,\mathrm{glec}}$ of the plectic Galois group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09475 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Équivalences de Fontaine multivariables Lubin-Tate et plectiques pour un corps local $p$-adique Marquis, Nataniel Number Theory Let $Δ$ be a finite set. We adapt the techniques of Carter-Kedlaya-Zábrádi to obtain a multivariable Fontaine equivalence which relates continuous finite dimensional $\mathbb{F}_q$-representations of $\prod_{α\in Δ} \mathcal{G}_{\mathbb{F}_q(\!(X)\!)}$ to multivariable $φ$-modules over a $\mathbb{F}_q$-algebra which is a domain. From this, we deduce a multivariable Lubin-Tate Fontaine equivalence for continuous finite type $\mathcal{O}_K$-representations of $\prod_{α\in Δ} \mathcal{G}_K$, where $K|\mathbb{Q}_p$ is a finite extension. We also obtain a plectic Fontaine equivalence and two equivalences for the subgroup $\mathcal{G}_{K,\mathrm{glec}}$ of the plectic Galois group. |
| title | Équivalences de Fontaine multivariables Lubin-Tate et plectiques pour un corps local $p$-adique |
| topic | Number Theory |
| url | https://arxiv.org/abs/2410.09475 |