Triviality in ideal class groups of Iwasawa-theoretical abelian number fields
Triviality in ideal class groups of Iwasawa-theoretical abelian number fields
复制标题
岩泽理论阿贝尔数域理想类群中的平凡性
DOI：
10.2969/jmsj/1158241937
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发表时间：
2005
影响因子：
0.7
通讯作者：
K. Horie
中科院分区：
文献类型：
--
作者：
K. Horie
.设S是素数的非空有限集，对S中的每个p，Zp表示p进整数环.设F是有理域上的阿贝尔扩张，使得F的有限次子域上的Galois群与Z p的直积的加法群拓扑同构，其中p为S中的任意p.我们将证明，每一个特定的算术级数只包含有限个素数l，对于这些素数l，F的l类群是非平凡的。这个结果暗示了我们在[ 3 ]中的猜想：F的l -类群为平凡的素数集合l在所有素数集合中具有自然密度1。
. Let S be a non-empty finite set of prime numbers and, for each p in S , let Z p denote the ring of p -adic integers. Let F be an abelian extension over the rational field such that the Galois group of F over some subfield of F with finite degree is topologically isomorphic to the additive group of the direct product of Z p for all p in S . We shall prove that each of certain arithmetic progressions contains only finitely many prime numbers l for which the l -class group of F is nontrivial. This result implies our conjecture in [ 3 ] that the set of prime numbers l for which the l -class group of F is trivial has natural density 1 in the set of all prime numbers.