The Structure of the Tame Kernels of Quadratic Number Fields (III)
The Structure of the Tame Kernels of Quadratic Number Fields (III)
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DOI：
10.1080/00927870701776797
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发表时间：
2008-03
影响因子：
0.7
通讯作者：
Xiaobin Yin;H. Qin;Q. Zhu
中科院分区：
文献类型：
--
作者：
Xiaobin Yin;H. Qin;Q. Zhu
设F是虚二次数域，K2OFF是F的驯服核.本文确定了每类虚二次数域F的r4（K2O F）的所有可能值特别是，对于每种类型的虚二次数域，我们给出了r 4（K 2 O F）的最大可能值，并证明了上下界之间的每个整数都是K 2 O F的4秩的值，对于无穷多个虚二次数域F.
Let F be an imaginary quadratic number field and K 2 O F the tame kernel of F. In this article, we determine all possible values of r 4(K 2 O F ) for each type of imaginary quadratic number field F. In particular, for each type of imaginary quadratic number field we give the maximum possible value of r 4(K 2 O F ) and show that each integer between the lower and upper bounds occurs as a value of the 4-rank of K 2 O F for infinitely many imaginary quadratic number fields F.