Cyclic polytopes and the K-theory of truncated polynomial algebras (with Ib Madsen)

In this paper, we give a formula, valid for any ring A, which exhibits the relative K-groups of a truncated polynomial algebra,
in terms of Bokstedt's topological Hochschild homology. In the case of a perfect field k of positive characteristic, this may be used to completely calculate the listed K-groups. Indeed, we show that
   K2m+1(k[x]/(xn),(x)) = W(m+1)n(k)/VnWm+1(k),
the even dimensional groups being zero. Here Wi(k) is the ring of big Witt vectors of length i, and Vn : Wi(k) &rarr Wni(k) is the nth Verschiebung map. The result extends previous calculations by Stienstra and Aisbett of K3(k[x]/(xn),(x)).

Lars Hesselholt <>
Ib Madsen <>