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>