Zariski density of crystalline points on $\GSp_{2n}$-valued local deformation rings
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929434929397760 |
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| author | Aoki, Kensuke |
| author_facet | Aoki, Kensuke |
| contents | We introduce trianguline deformation spaces $X_{\tri} (\overlineρ)$ for a $\GSp_{2n}$-valued residual representation $\overlineρ \colon {\mathcal{G}}_K \to \GSp_{2n} (k)$, where $k$ is a finite field of characteristic $p > 0$ and ${\mathcal{G}}_K$ is the absolute Galois group of a finite extension $K / {\mathbb{Q}}_p$, and study their properties. We show Zariski density of the crystalline points on the rigid generic fiber ${\mathfrak{X}}_{\overlineρ}$ of the framed deformation space of $\overlineρ$ under some conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_17005 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Zariski density of crystalline points on $\GSp_{2n}$-valued local deformation rings Aoki, Kensuke Number Theory We introduce trianguline deformation spaces $X_{\tri} (\overlineρ)$ for a $\GSp_{2n}$-valued residual representation $\overlineρ \colon {\mathcal{G}}_K \to \GSp_{2n} (k)$, where $k$ is a finite field of characteristic $p > 0$ and ${\mathcal{G}}_K$ is the absolute Galois group of a finite extension $K / {\mathbb{Q}}_p$, and study their properties. We show Zariski density of the crystalline points on the rigid generic fiber ${\mathfrak{X}}_{\overlineρ}$ of the framed deformation space of $\overlineρ$ under some conditions. |
| title | Zariski density of crystalline points on $\GSp_{2n}$-valued local deformation rings |
| topic | Number Theory |
| url | https://arxiv.org/abs/2407.17005 |