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.

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