论文标题
$ p $ adiC局部单曲霉定理的群体理论概括
A group-theoretic generalization of the $p$-adic local monodromy theorem
论文作者
论文摘要
让$ g $为$ p $ - adic本地字段$ f $的连接还原组。我们提出和研究$ g $ - $φ$ - 模型和$ g $ - $（φ，\ nabla）$ - Robba戒指上的模块，这是$ g $ g $ g $ f $ f $ f $ f $ f $ f $ -vector $ -vector $ -vector $ -vector $ -vector $ -v $ $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ -vector $ -vector $ -veul $ -veul $ -v $ - $ - $ - $ - $（φ，\ nabla）$ - 在Robba环上的模块，分别与各个光纤函子通勤。我们在这种情况下研究Kedlaya的斜率过滤定理，并表明Robba环上的$ G $ - $（φ，\ nabla）$ - 模块是“ $ g $ -Quasi-Unipotent”，这是$ P $ P $ -P $ -ADIC本地单型单型单型原理的概括。
Let $G$ be a connected reductive group over a $p$-adic local field $F$. We propose and study the notions of $G$-$φ$-modules and $G$-$(φ,\nabla)$-modules over the Robba ring, which are exact faithful $F$-linear tensor functors from the category of $G$-representations on finite-dimensional $F$-vector spaces to the categories of $φ$-modules and $(φ,\nabla)$-modules over the Robba ring, respectively, commuting with the respective fiber functors. We study Kedlaya's slope filtration theorem in this context, and show that $G$-$(φ,\nabla)$-modules over the Robba ring are "$G$-quasi-unipotent", which is a generalization of the $p$-adic local monodromy theorem proven independently by Y. André, K. S. Kedlaya, and Z. Mebkhout.
