### On the K-theory of local fields, by Lars Hesselholt and Ib Madsen

This preprint has been updated (see 0550) and the dvi
files for this version have been removed.

Let K be a complete discrete valuation field of char. 0 with perfect
residue field of char. p > 2. We establish a connection between the
K-theory of K and the de Rham-Witt complex of the valuation ring O_{K}
with logarithmic poles at the maximal ideal. We use this to show that
for s >= 1,

K_{2s}(K,Z/p^{v}Z) = H^{0}(K,Z/p^{v}Z(s)) + H^{2}(K,Z/p^{v}Z(s+1)),

K_{2s+1}( K,Z/p^{v}Z) = H^{1}(K,Z/p^{v}Z(s+1)).

This confirms the Licthenbaum-Quillen conjecture for the field K.

Lars Hesselholt <larsh@math.mit.edu>

Ib Madsen <imadsen@imf.au.dk>