Rigid Character Groups, Lubin-Tate Theory, and (phi, Gamma) -Modules
Rigid Character Groups, Lubin-Tate Theory, and (phi, Gamma) -Modules
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刚性字符组、Lubin-Tate 理论和 (phi, Gamma) -模块
DOI：
10.1090/memo/1275
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发表时间：
2020
影响因子：
1.9
通讯作者：
Xie Bingyong
中科院分区：
文献类型：
--
作者：
Berger Laurent;Schneider Peter;Xie Bingyong
- adic局部Langlands对应的构造在本质上应用了方丹的分圆模理论。这里分圆是指的分圆扩张的伽罗瓦群。为了推广的进局部朗兰兹对应，其中是一个有限的扩展，它似乎有必要在我们的处置一个理论的Lubin-Tate模。这样的推广已经在一定程度上进行了，通过工作在-adic开单位盘，赋予的作用的自同态的Lubin-Tate群。本文的主要思想是以一种不同的方式对分圆模理论进行Lubin-Tate推广。而不是进开单位盘，我们的工作在一个字符的品种，参数化的本地分析字符。我们研究的模块在这种设置，并与他们中的一些是以前已知的。
The construction of the-adic local Langlands correspondence foruses in an essential way Fontaine’s theory of cyclotomic-modules. Here cyclotomic means thatis the Galois group of the cyclotomic extension of. In order to generalize the-adic local Langlands correspondence to, whereis a finite extension of, it seems necessary to have at our disposal a theory of Lubin-Tate-modules. Such a generalization has been carried out to some extent, by working over the-adic open unit disk, endowed with the action of the endomorphisms of a Lubin-Tate group. The main idea of our article is to carry out a Lubin-Tate generalization of the theory of cyclotomic-modules in a different fashion. Instead of the-adic open unit disk, we work over a character variety, that parameterizes the locally-analytic characters on. We study-modules in this setting, and relate some of them to what was known previously.