### The tower of K-theory of truncated polynomial algebras

Let A a regular **F**_{p}-algebra. The relative K-groups
K_{q}(A[x]/(x^{m}),(x)) and the Nil-groups
Nil_{q}(A[x]/(x^{m})) were evaluated earlier by the
author and Madsen in terms of the big de Rham-Witt groups of the ring
A. In this paper, we evaluate the maps of relative K-groups and
Nil-groups induced by the canonical projection f :
A[x]/(x^{m}) &rarr A[x]/(x^{n}). The result depends
strongly on the prime *p*. It generalizes work of Stienstra on
the groups in degrees 2 and 3.

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