论文标题
关于代数整数的$ k $ groups的结构
On the structure of even $K$-groups of rings of algebraic integers
论文作者
论文摘要
在本文中，我们描述了一个数字字段的适当扩展的班级组的较高数字字段整数环的$ k $ - 组。这是Browkin，Keune和Kolster以前的集体作品的自然扩展，他们考虑了$ K_2 $的情况。然后，我们重新审视了库默（Kummer）对格林伯格（Greenberg）和基达（Kida）概括的完全真实领域的标准。特别是，我们给出了代数$ k $ - 该标准的理论表述，我们将使用此处开发的代数$ k $ - 理论结果证明。
In this paper, we describe the higher even $K$-groups of the ring of integers of a number field in terms of class groups of an appropriate extension of the number field in question. This is a natural extension of the previous collective works of Browkin, Keune and Kolster, where they considered the case of $K_2$. We then revisit the Kummer's criterion of totally real fields as generalized by Greenberg and Kida. In particular, we give an algebraic $K$-theoretical formulation of this criterion which we will prove using the algebraic $K$-theoretical results developed here.
