### On the K-theory of complete regular local F_{p}-algebras
(with Thomas Geisser)

In this paper we prove continuity of K-theory with
**Z**/p^{v}-coefficients for a complete regular local
**F**_{p}-algebra, provided that the residue field has a
finite *p*-basis. This restriction on the residue field is
very mild. The corresponding statement with **Z**/m-coefficients,
*m* prime to *p*, follows from Gabber-Suslin rigidity.
In the proof we give a formula, interesting in its own right, for the
de Rham-Witt complex of a power series ring A[[x]]. The formula is
valid whenever A is a noetherian **F**_{p}-algebra which as
a module over the subring A^{p} of *p*th powers is
finitely generated.

Thomas Geisser <geisser@math.usc.edu>
Lars Hesselholt <larsh@math.mit.edu>