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

Acta Arithmetica 211 (2023) , No. 4, 345-361 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,...

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Bibliographic Details
Main Author Lim, Meng Fai
Format Journal Article
LanguageEnglish
Published 30.09.2022
Subjects
Mathematics - Number Theory
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Summary:Acta Arithmetica 211 (2023) , No. 4, 345-361 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.
DOI:10.48550/arxiv.2210.00168