On the image of noncommutative local reciprocity map
On the image of noncommutative local reciprocity map
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DOI：
10.4310/hha.2005.v7.n3.a4
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
I. Fesenko
中科院分区：
文献类型：
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作者：
I. Fesenko
算术非交换局部类场论方向的第一步在[2]中被描述为试图找到经典阿贝尔类场论的算术推广;见[3]对其主要特征的阐述。特别地，[2]澄清和简化了H. Koch和E.德沙利特[7]，[8].在非交换局部类场论[2]中，利用全分歧算术有限Galois扩张L/F的Galois群Gal（L/F）与F的剩余域的代数闭包上的一元形式幂级数的某个子商之间的非交换互反映射，给出了固定局部域F的Galois扩张的直接算术描述（更确切地说，它是L/F的范数域的极大非分歧扩张的完备化）。其中一个互易图（定义见下文）是
First steps in the direction of an arithmetic noncommutative local class field theory were described in [2] as an attempt to find an arithmetic generalization of the classical abelian class field theory; see [3] for an exposition of its main features. In particular, [2] clarified and simplified the metabelian local class field theory of H. Koch and E. de Shalit [7], [8]. In the noncommutative local class field theory [2] a direct arithmetic description of Galois extensions of a fixed local field F is given by means of noncommutative reciprocity maps between the Galois group Gal(L/F ) of a totally ramified arithmetically profinite Galois extension L/F and a certain subquotient of formal power series in one variable over the algebraic closure of the residue field of F (which, more precisely, is the completion of the maximal unramified extension of the field of norms of L/F ). One of the reciprocity maps (see below for definitions) is