On the K-theory of complete regular local Fp-algebras

LetA be a noetherian F-p-algebra that is finitely generated as a module over the subring A(p) of pth powers. We give an explicit formula for the de Rham-Witt complex of the power series ring A[t] in terms of that of the ring A. We use this formula to show that, for every complete regular local F-p-algebra whose residue field is a finite extension of the subfield of pth powers, the canonical map from the algebraic K-theory with Z/p(nu)-coefficients to the topological K-theory with Z/p(nu)-coefficients is an isomorphism. (C) 2005 Elsevier Ltd. All rights reserved.