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

@article{Geisser2003TheDR,
title={The de Rham-Witt complex and p-adic vanishing cycles},
author={Thomas H. Geisser and Lars Hesselholt},
journal={Journal of the American Mathematical Society},
year={2003},
volume={19},
pages={1-36}
}
• Published 30 December 2003
• Mathematics
• Journal of the American Mathematical Society
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…
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