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>