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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.00389 |
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| _version_ | 1866912018521391104 |
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| author | Wang, Yitong |
| author_facet | Wang, Yitong |
| contents | Let $p$ be a prime number, $K$ a finite unramified extension of $\mathbb{Q}_p$ and $\mathbb{F}$ a finite extension of $\mathbb{F}_p$. For $π$ an admissible smooth representation of $\operatorname{GL}_2(K)$ over $\mathbb{F}$ satisfying certain multiplicity-one properties, we compute the rank of the associated étale $(φ,\mathcal{O}_K^{\times})$-module $D_A(π)$ defined by Breuil-Herzig-Hu-Morra-Schraen, extending their results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_00389 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the rank of the multivariable $(φ,\mathcal{O}_K^{\times})$-modules associated to mod $p$ representations of $\operatorname{GL}_2(K)$ Wang, Yitong Number Theory Let $p$ be a prime number, $K$ a finite unramified extension of $\mathbb{Q}_p$ and $\mathbb{F}$ a finite extension of $\mathbb{F}_p$. For $π$ an admissible smooth representation of $\operatorname{GL}_2(K)$ over $\mathbb{F}$ satisfying certain multiplicity-one properties, we compute the rank of the associated étale $(φ,\mathcal{O}_K^{\times})$-module $D_A(π)$ defined by Breuil-Herzig-Hu-Morra-Schraen, extending their results. |
| title | On the rank of the multivariable $(φ,\mathcal{O}_K^{\times})$-modules associated to mod $p$ representations of $\operatorname{GL}_2(K)$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2404.00389 |