On the KK-theory of complete regular local FpFp-algebras

Let A   be a noetherian FpFp-algebra that is finitely generated as a module over the subring ApAp of p  th powers. We give an explicit formula for the de Rham–Witt complex of the power series ring A〚t〛A〚t〛 in terms of that of the ring A  . We use this formula to show that, for every complete regular local FpFp-algebra whose residue field is a finite extension of the subfield of pth powers, the canonical map from the algebraic K  -theory with Z/pvZ/pv-coefficients to the topological K  -theory with Z/pvZ/pv-coefficients is an isomorphism.