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^vZ) = H⁰(K,Z/p^vZ(s)) + H²(K,Z/p^vZ(s+1)),

K_2s+1( K,Z/p^vZ) = H¹(K,Z/p^vZ(s+1)).

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

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