On the K-theory of complete regular local Fp-algebras
(with Thomas Geisser)
In this paper we prove continuity of K-theory with
Z/pv-coefficients for a complete regular local
Fp-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 Fp-algebra which as
a module over the subring Ap of pth powers is
finitely generated.
Lars Hesselholt <larsh@math.nagoya-u.ac.jp>