On the torsion part in the K-theory of imaginary quadratic fields

TL;DR

This paper provides upper bounds on the torsion in the K-groups of imaginary quadratic fields' rings of integers, relating these bounds to the fields' discriminants, advancing understanding of algebraic K-theory in number fields.

Contribution

It introduces new upper bounds for torsion in K-groups of imaginary quadratic fields based on their discriminants, a novel quantitative approach.

Findings

Upper bounds for torsion in K-groups established

Bounds expressed in terms of discriminants

Advances understanding of algebraic K-theory in quadratic fields

Abstract

We obtain upper bounds for the torsion in the $K$-groups of the ring of integers of imaginary quadratic number fields, in terms of their discriminants.