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Journal of Topology Advance Access originally published online on October 25, 2007
Journal of Topology 2008 1(1):87-114; doi:10.1112/jtopol/jtm007
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© 2007 London Mathematical Society

The tower of K-theory of truncated polynomial algebras

Lars Hesselholt

Lars Hesselholt, Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, USA, larsh{at}math.mit.edu
Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan, larsh{at}math.nagoya-u.ac.jp


  Abstract

Let A be a regular noetherian Fp-algebra. The relative K-groups Kq(A[x]/(xm),(x)) and the Nil-groups Nilq(A[x]/(xm)) were evaluated by the author and Ib Madsen in terms of the big de Rham–Witt groups Wr{Omega}Aq 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) -> A[x]/(xn). The result depends strongly on the prime p. It generalizes earlier work by Stienstra on the groups in degrees 2 and 3.

Received February 28, 2007.

2000 Mathematics Subject Classification 19D55 (primary), 19E15 (secondary)

Research supported in part by the National Science Foundation.


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