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arXiv · 2210.00168

On the structure of even $K$-groups of rings of algebraic integers

Meng Fai Lim
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Abstract

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.

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Meng Fai Lim. 2023-08-08. On the structure of even $K$-groups of rings of algebraic integers. https://doi.org/10.4064/aa221029-25-7

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