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 WmΩA
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.nagoya-u.ac.jp>