Lyndon-Demushkin method and crystalline lifts of $G_2$-valued Galois representations
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arXiv
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866929730191622144 |
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| author | Lin, Zhongyipan |
| author_facet | Lin, Zhongyipan |
| contents | We show for all local fields $K/\mathbb{Q}_p$, with $p >3$, all representations $\barρ:G_K \to G_2(\bar{\mathbb{F}}_p)$ admit a crystalline lift $ρ: G_K\to G_2(\bar{\mathbb{Z}}_p)$, where $G_2$ is the exceptional Chevalley group of type $G_2$.
The main ingredient is a new technique for analyzing the obstruction of non-abelian extensions of Galois modules, which has roots in combinatorial group theory. We also rely on the Emerton-Gee stack of $(ϕ, Γ)$-modules to construct abelian extensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_08773 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Lyndon-Demushkin method and crystalline lifts of $G_2$-valued Galois representations Lin, Zhongyipan Number Theory 11F80 We show for all local fields $K/\mathbb{Q}_p$, with $p >3$, all representations $\barρ:G_K \to G_2(\bar{\mathbb{F}}_p)$ admit a crystalline lift $ρ: G_K\to G_2(\bar{\mathbb{Z}}_p)$, where $G_2$ is the exceptional Chevalley group of type $G_2$. The main ingredient is a new technique for analyzing the obstruction of non-abelian extensions of Galois modules, which has roots in combinatorial group theory. We also rely on the Emerton-Gee stack of $(ϕ, Γ)$-modules to construct abelian extensions. |
| title | Lyndon-Demushkin method and crystalline lifts of $G_2$-valued Galois representations |
| topic | Number Theory 11F80 |
| url | https://arxiv.org/abs/2011.08773 |