On the K-theory of complete regular local F_p-algebras, by Thomas Geisser and Lars Hesselholt

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 is finitely generated.

Thomas Geisser <geisser@ms.u-tokyo.ac.jp>
Lars Hesselholt <larsh@math.mit.edu>