Reflection Theorems and the Tame Kernel of a Number Field
Reflection Theorems and the Tame Kernel of a Number Field
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DOI：
10.1080/00927872.2013.772188
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发表时间：
2014-03
影响因子：
0.7
通讯作者：
Xia Wu;Zhengjun Zhao
中科院分区：
文献类型：
--
作者：
Xia Wu;Zhengjun Zhao
设L是含有单位ζp的第p个本原根的数域。利用反射定理研究了L的某些子域的理想类群的p-秩.建立了理想类群的p-秩与L的某些子域的单位群的p-秩间的关系.设F是数域，𝒪F是F中的整数环.研究了F的驯服核的p-秩.建立了K2𝒪F的p-秩与F(ζp)的理想类群的一些直和子群的p-秩间的关系.
Let L be a number field containing the pth primitive root of unity ζ p . We investigate the p-rank of the ideal class groups of some subfields of L by using reflection theorems and establish relations between the p-rank of the ideal class groups and that of groups of units of some subfields of L. Let F be a number field and 𝒪 F the ring of integers in F. We also study the p-rank of tame kernels of F and establish relations between the p-rank of K 2𝒪 F and that of some direct summands of the ideal class group of F(ζ p ).