Let K be a complete discrete valuation field of char. 0 with perfect
residue field of odd characteristic p. 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 greater than or
equal to 1,
K2s(K, Z/pv Z) =
H0(K, Z/pv Z(s)) +
H2(K, Z/pv Z(s+1)),
K2s+1(K, Z/pv Z) =
H1(K, Z/pv Z(s+1)).
This confirms the Licthenbaum-Quillen conjecture for the field K.
Lars Hesselholt <firstname.lastname@example.org>
Ib Madsen <email@example.com>