On the K-theory of truncated polynomial algebras over the integers

We show that K2i(Z[x]/(xm),(x)) is finite of order (mi)!(i!)m-2 and that K2i+1(Z[x]/(xm),(x)) is free abelian of rank m-1. This is accomplished by showing that the equivariant homotopy groups TRnq-&lambda(Z;p) of the topological Hochschild T-spectrum are free abelian, if q is even, and finite, if q is odd, and by determining their ranks and orders, respectively.

Lars Hesselholt <larsh@math.nagoya-u.ac.jp>