On the algebraic K-theory of the coordinate axes over the integers

TL;DR

This paper computes specific algebraic K-groups of the coordinate axes over integers, revealing their structure as free abelian or finite groups, and provides explicit calculations in low degrees.

Contribution

It determines the algebraic K-theory groups of the coordinate axes over integers, including their ranks and orders, and computes low-degree cases explicitly.

Findings

K_{2i}(Z[x,y]/(xy),(x,y)) is free abelian of rank 1

K_{2i+1}(Z[x,y]/(xy),(x,y)) is finite of order (i!)^2

Explicit calculations of K_{2i+1} in low degrees

Abstract

We show that K_{2i}(Z[x,y]/(xy),(x,y)) is free abelian of rank 1 and that K_{2i+1}(Z[x,y]/(xy),(x,y)) is finite of order (i!)^2. We also compute K_{2i+1}(Z[x,y]/(xy),(x,y)) in low degrees.