p-adic Hodge parameters in the crystalline representations of GSp4
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915655859568640 |
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| author | Han, Xiaozheng |
| author_facet | Han, Xiaozheng |
| contents | This article gives a generalization of the work of Y.Ding in the context of $\mathrm{GSp}_4(\mathbb{Q}_p)$, where $p$ is an odd prime number. Let $ρ$ be a 4-dimensional generic non-critical crystalline representations of the absolute Galois group of $\mathbb{Q}_p$ of regular Hodge-Tate weights which is valued in $\mathrm{GSp}_4(E)$, where $E$ is a finite extension of $\mathbb{Q}_p$, we associate to $ρ$ an explicit locally analytic $E$-representation $π_\mathrm{min}(ρ)$ of $\mathrm{GSp}_4(\mathbb{Q}_p)$, which encodes enough information to determines $ρ$. Moreover, under certain settings, this construction follows the local-global compatibility. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_05275 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | p-adic Hodge parameters in the crystalline representations of GSp4 Han, Xiaozheng Number Theory Representation Theory This article gives a generalization of the work of Y.Ding in the context of $\mathrm{GSp}_4(\mathbb{Q}_p)$, where $p$ is an odd prime number. Let $ρ$ be a 4-dimensional generic non-critical crystalline representations of the absolute Galois group of $\mathbb{Q}_p$ of regular Hodge-Tate weights which is valued in $\mathrm{GSp}_4(E)$, where $E$ is a finite extension of $\mathbb{Q}_p$, we associate to $ρ$ an explicit locally analytic $E$-representation $π_\mathrm{min}(ρ)$ of $\mathrm{GSp}_4(\mathbb{Q}_p)$, which encodes enough information to determines $ρ$. Moreover, under certain settings, this construction follows the local-global compatibility. |
| title | p-adic Hodge parameters in the crystalline representations of GSp4 |
| topic | Number Theory Representation Theory |
| url | https://arxiv.org/abs/2512.05275 |