Unramified class field theory of arithmetical surfaces
Unramified class field theory of arithmetical surfaces
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算术曲面的无分支域论
DOI：
10.2307/1971173
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发表时间：
1983
影响因子：
4.9
通讯作者：
S. Saito
中科院分区：
文献类型：
--
作者：
Kazuya Kato;S. Saito
设k是一个代数数域，（9 k）是它的整数环，V是Spec（Ck）的非空子概型.设X是k上的射影光滑几何不可约格式，X是V上的正则真平坦格式，使得XxVkX.本文的目的是用K-理论的方法，利用X和X上的一些“理想类群”，给出交换基本群ab（X）和7 T B（X）的一个明确的描述.其概要如下：一般地，对于Noether概型Z且i = 0或1，我们定义群SKi（Z）为
Let k be an algebraic number field, (9k its ring of integers and V a non-empty open subscheme of Spec(Ck). Let X be a projective smooth geometrically irreducible scheme over k, and X a regular proper flat scheme over V such that X x Vk X. The purpose of this paper is to give an explicit description of the abelian fundamental groups ,ab (X) and 7T b(X), using some "idele class groups" attached to X and X by a K-theoretical method. Its outline is as follows: In general, for a noetherian scheme Z and i = 0 or 1, we define the group SKi(Z) to be the cokernel of