On the K-theory of complete regular local Fp-algebras

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