The tower of K-theory of truncated polynomial algebras

Let A a regular Fp-algebra. The relative K-groups Kq(A[x]/(xm),(x)) and the Nil-groups Nilq(A[x]/(xm)) 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]/(xm) &rarr A[x]/(xn). 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.mit.edu>