On the -theory of complete regular local -algebras

Let A be a noetherian F p -algebra that is finitely generated as a module over the subring A p 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 F p -algebra whose residue field is a finite extension of the subfield of pth powers, the canonical map from the algebraic K-theory with Z / p v -coefficients to the topological K-theory with Z / p v -coefficients is an isomorphism.