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 OK with logarithmic poles at the maximal ideal. We use this to show that for s >= 1,

K2s(K,Z/pvZ) = H0(K,Z/pvZ(s)) + H2(K,Z/pvZ(s+1)),

K2s+1( K,Z/pvZ) = H1(K,Z/pvZ(s+1)).

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

Lars Hesselholt <larsh@math.mit.edu>
Ib Madsen <imadsen@imf.au.dk>