Kato's higher local class field theory
Kato's higher local class field theory
复制标题
加藤的高等局部类场论
DOI：
10.2140/gtm.2000.3.53
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发表时间：
2000
影响因子：
0.8
通讯作者：
M. Kurihara
中科院分区：
文献类型：
--
作者：
M. Kurihara
我们首先回顾经典的局部阶级场理论。设K是Qp或Fq（(X)）的有限扩展。局部类场论的主要定理包括同构定理和存在定理。在本节中，我们考虑同构定理。其中一个证明的大纲如下。首先，对于Br(K)群，建立了Br(K)→Q/Z的同构逆；主要由一个同构H1（F, Q/Z）→Q/Z推导而来，其中ef为k的残馀域。其次，用XK = Homcont（GK, Q/Z）表示GK = Gal（K/K）到Q/Z的连续同态群。我们考虑一对K × XK−→Q/Z
We first recall the classical local class field theory. Let K be a finite extension of Qp or Fq((X)). The main theorem of local class field theory consists of the i somorphism theorem and existence theorem. In this section we consider t he isomorphism theorem. An outline of one of the proofs is as follows. First, for the Br auer groupBr(K), an isomorphism inv: Br(K) →̃Q/Z is established; it mainly follows from an isomorphism H1(F, Q/Z) →̃Q/Z whereF is the residue field ofK . Secondly, we denote by XK = Homcont(GK , Q/Z) the group of continuous homomorphisms fromGK = Gal(K/K) to Q/Z. We consider a pairing K × XK −→ Q/Z