论文标题
Lyndon-Demushkin方法和$ g_2 $ - 价值的galois表示的结晶升降机
Lyndon-Demushkin method and crystalline lifts of $G_2$-valued Galois representations
论文作者
论文摘要
我们为所有本地字段显示$ k/\ mathbb {q} _p $，$ p> 3 $，所有表示$ \barρ：g_k \ to g_2（\ bar {\ mathbb {f}} _ p） $ g_2 $是类型$ G_2 $的奇特雪佛莉组。 主要成分是一种新技术，用于分析Galois模块的非亚洲扩展的阻塞，该技术源于组合群体理论。我们还依靠$（ϕ，γ）$ - 模块的Emerton-Gee堆栈来构建Abelian扩展。
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.
