K-theory for ring C*-algebras attached to function fields with only one infinite place

TL;DR

This paper investigates the K-theory of ring C*-algebras linked to rings of integers in global function fields with one infinite place, revealing how torsion in K-theory encodes inertia degrees under certain conditions.

Contribution

It computes the torsion-free K-groups of these C*-algebras and shows that torsion parts determine inertia degrees under a primeness condition.

Findings

Computed torsion-free K-groups for these C*-algebras.

Established that torsion in K-theory encodes inertia degrees.

Demonstrated the significance of a primeness condition in this relationship.

Abstract

We study the K-theory of ring C*-algebras associated to rings of integers in global function fields with only one single infinite place. First, we compute the torsion-free part of the K-groups of these ring C*-algebras. Secondly, we show that, under a certain primeness condition, the torsion part of K-theory determines the inertia degrees at infinity of our function fields.