论文标题
本地分析向量和周期的环
Locally analytic vectors and rings of periods
论文作者
论文摘要
在本文中，我们尝试使用局部分析矢量来扩展Berger和Colmez的观点，以便在更高的时期范围内概括经典的环流理论。我们还解释了局部分析载体的形式主义如何恢复Colmez的环$ \ Mathbf {b} _ {sen} $，并在de rham案中扩展到sen理论，并延伸到古典$（φ，γ）$ - 模块理论。我们解释了当我们试图将$（φ，γ）$ - 模块的构建体概括为任意无限分支$ p $ ad的谎言扩展时会发生什么，并就相应环中局部分析矢量的结构提供了猜想。我们还强调了这样一个事实，即情况应大不相同，具体取决于$ p $ - adiC的谎言扩展``````````'''最后，我们解释了其中一些结构如何与三角形时期环的构造有关。
In this paper, we try to extend Berger's and Colmez's point of view, using locally analytic vectors in order to generalize classical cyclotomic theory, in higher rings of periods. We also explain how the formalism of locally analytic vectors recovers the ring $\mathbf{B}_{Sen}$ of Colmez, and extends to Sen theory in the de Rham case, and to classical $(φ,Γ)$-modules theory. We explain what happens when we try to generalize constructions of $(φ,Γ)$-modules to arbitrary infinitely ramified $p$-adic Lie extensions, and provide a conjecture on the structure of the locally analytic vectors in the corresponding rings. We also highlight the fact that the situation should be very different, depending on wether the $p$-adic Lie extension ``contains a cyclotomic extension'' or not. Finally, we explain how some of these constructions may be related to the construction of a ring of trianguline periods.
