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

摘要

We show that the relative algebraic $K$-theory group $K_{2i}(mathbb{Z}[x, y]/(xy), (x, y))$ is free abelian of rank 1 and that $K_{2i+1}(mathbb{Z}[x, y]/(xy), (x, y))$ is finite of order $(i!)^2$. We also find the group structure of $K_{2i+1}(mathbb{Z}[x, y]/(xy), (x, y))$ in low degrees.