On Zℓ-extensions of algebraic number fields: Ann. of Math., (2) 98 (1973), 246–326
On Zℓ-extensions of algebraic number fields: Ann. of Math., (2) 98 (1973), 246–326
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关于代数数域的 Zℓ 扩展：Ann. of Math., (2) 98 (1973), 246–326
DOI：
10.1007/978-4-431-67947-9_52
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
S. Nakajima
中科院分区：
文献类型：
--
作者：
I. Satake;Genjiro Fujisaki;Kazuya Kato;M. Kurihara;S. Nakajima
设l是一个素数，在下面的讨论中它是固定不变的，设Zl表示所有l-adic整数的环。域k的伽罗瓦扩张K称为k上的Zl-扩张，如果伽罗瓦群Gal（K/k）拓扑同构于紧环Zl 1的加群.在本文中，我们将研究算术性质的情况下，基域是有限的代数数域的Z l-扩张。
Let l be a prime number which will be fixed throughout the following, and let Z l denote the ring of all l-adic integers. A Galois extension K of a field k is called a Z l-extension over k if the Galois group Gal (K/k) is topologically isomorphic to the additive group of the compact ring Z l 1. In the present paper, we shall study arithmetic properties of such Z l-extensions in the case where the ground fields are finite algebraic number fields.