The tower of K-theory of truncated polynomial algebras

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]/(xⁿ). The result depends strongly on the prime p. It generalizes work of Stienstra on the groups in degrees 2 and 3.

tower.pdf [July 25, 2007]
An additional graphics illustration.

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