On even $K$-groups of rings of integers of real abelian fields

Meng Fai Lim; Chao Qin

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arXiv · 2509.13796

On even $K$-groups of rings of integers of real abelian fields

Meng Fai Lim·Chao Qin

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Abstract

We present approaches for calculating the precise orders of the algebraic $K$-groups $K_{4n-2}(\mathcal{O}_K)$ for a totally real abelian $K$. Along the way, we also establish a formula connecting the order of $K_{4n-2}(\mathcal{O}_E)$ of a totally real $p$-elementary field $E$ to its intermediate cyclic $p$-degree fields. Additionally, we provide a compiled list of values for these $K$-groups.

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Meng Fai Lim, Chao Qin. 2025-09-17. On even $K$-groups of rings of integers of real abelian fields. https://arxiv.org/abs/2509.13796

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