### On the K-theory of nilpotent endomorphisms (with Ib Madsen)

Let A be a smooth algebra over a perfect field k of positive
characteristic *p*. This paper evaluates
K_{*}(A[x]/(x^{n}),(x)) in terms of the big de
Rham-Witt complex **W**_{m}&Omega_{A}^{*}
of the ring A. The result generalized the case A = k, which
was treated in an earlier paper. We use this to evaluate the of the
groups Nil_{*}(A[x]/(x^{n})). The result again is
given in terms of big de Rham-Witt complexes. When A is a polynomial
algebra the structure of these groups is completely known.

Lars Hesselholt <larsh@math.mit.edu>
Ib Madsen <imadsen@imf.au.dk>