On the algebraic $K$-theory of the Hilbert modular group

TL;DR

This paper provides formulas for Whitehead groups and rational K-theory groups of the Hilbert modular group using its maximal finite subgroups, advancing understanding of its algebraic K-theory.

Contribution

It introduces explicit formulas relating the algebraic K-theory of the Hilbert modular group to its finite subgroups, a novel approach in the field.

Findings

Formulas for Whitehead groups derived.

Rational K-theory groups expressed in terms of finite subgroups.

Enhanced understanding of the algebraic K-theory of Hilbert modular groups.

Abstract

We give formulas for the Whitehead groups and the rational $K$-theory groups of the (integer group ring of the) Hilbert modular group in terms of its maximal finite subgroups.