The de Rham-Witt complex and p-adic vanishing cycles

Details The de Rham-Witt complex and p-adic vanishing cycles The de Rham-Witt complex and p-adic vanishing cycles

2003-12-30

arxiv.org/abs/math/0312497v3

J. Amer. Math. Soc. 19 (2006), 1-36.

Mathematics

Number Theory

Scientific paper

We determine the structure modulo p 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 together with results of the second author and Madsen to evaluate the $K$-theory with finite 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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