论文标题
SEN运营商和谎言代数由Galois代表产生，超过$ P $ ADIC品种
Sen Operators and Lie Algebras arising from Galois Representations over $p$-adic Varieties
论文作者
论文摘要
任何有限维$ p $ p $ adiC的代表是绝对Galois集团的$ p $ - adiC本地田地，其残留物缺陷的特征是其算术和几何SEN操作员由Sen和Brinon定义。我们将它们的结构推广到具有半稳定图表的$ p $ addic仿射品种的基本组，并证明了Sen运营商的模块是规范定义的，与图表的选择无关。我们的建筑依赖于Tsuji开发的$ p $ -Adic Simpson通信中的下降定理。当该表示来自$ \ Mathbb {Q} _p $ - 代表$ P $ -ADIC分析小组的商人，我们将根据SEN操作员来描述其Lie代数行动，这是Sen和Ohkubo的结果。这些参议员可以连续扩展到某些无限尺寸表示。作为应用程序，我们证明了几何SEN操作员在局部分析载体中消灭了PAN的结果。
Any finite-dimensional $p$-adic representation of the absolute Galois group of a $p$-adic local field with imperfect residue field is characterized by its arithmetic and geometric Sen operators defined by Sen and Brinon. We generalize their construction to the fundamental group of a $p$-adic affine variety with a semi-stable chart, and prove that the module of Sen operators is canonically defined, independently of the choice of the chart. Our construction relies on a descent theorem in the $p$-adic Simpson correspondence developed by Tsuji. When the representation comes from a $\mathbb{Q}_p$-representation of a $p$-adic analytic group quotient of the fundamental group, we describe its Lie algebra action in terms of the Sen operators, which is a generalization of a result of Sen and Ohkubo. These Sen operators can be extended continuously to certain infinite-dimensional representations. As an application, we prove that the geometric Sen operators annihilate locally analytic vectors, generalizing a result of Pan.
