Finiteness theorems in the class field theory of varieties over local fields
Finiteness theorems in the class field theory of varieties over local fields
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局部域上簇的类域论中的有限定理
DOI：
10.1016/s0022-314x(03)00018-0
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发表时间：
2003
影响因子：
0.7
通讯作者：
Teruyoshi Yoshida
中科院分区：
文献类型：
--
作者：
Teruyoshi Yoshida
我们证明了局部域上一个适当光滑变种的阿贝尔氏<s:1>基本群的几何部分是有限地在Z *上产生的，并且用Albanese变种的nsamron模型的特殊纤维描述了它的秩。作为一个应用，我们完成了Bloch和Saito提出的局部场上曲线的类场论，其中关于正特征情况下p初等部的定理仍然没有得到证明。
We show that the geometrical part of the abelian étale fundamental group of a proper smooth variety over a local field is finitely generated over Z ̂ with finite torsion, and describe its rank by the special fiber of the Néron model of the Albanese variety. As an application, we complete the class field theory of curves over local fields developed by Bloch and Saito, in which the theorem concerning the p-primary part in the positive characteristic case has remained unproven.