### The de Rham-Witt complex and p-adic vanishing cycles, by Thomas Geisser and Lars Hesselholt

We determine the structure of the de Rham-Witt complex of a smooth
scheme X over a discrete valuation ring of mixed characteristic with
log-poles along the special fiber Y and show that the sub-sheaf fixed
by the Frobenius is isomorphic to the sheaf of p-adic vanishing
cycles. We use this result to evaluate the algebraic K-theory
with coefficients of the quotient field K of the henselian local
ring of X at a generic point of Y. The result affirms the
Lichtenbaum-Quillen conjecture for the field K.

Thomas Geisser <geisser@math.usc.edu>

Lars Hesselholt <larsh@math.mit.edu>