Cyclic polytopes and the K-theory of truncated polynomial algebras, by Lars Hesselholt and 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,
n
K (A[x]/(x ),(x))
*
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
n
K (k[x]/(x ),(x)) = W (k)/V W (k)
2m-1 nm-1 n m-1
the even dimensional groups being zero. Here
W (k)
i
is the ring of big Witt vectors of length i. The result extends previous
calculations by Stienstra and Aisbett of
n
K (k[x]/(x ),(x)).
3
Lars Hesselholt <larsh@math.mit.edu>
Ib Madsen <imadsen@mi.aau.dk>