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| Main Author: | |
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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2011.08773 |
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Table of 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.