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]/(xn),(x)) in terms of the big de Rham-Witt complex Wm&OmegaA* 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]/(xn)). 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>