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}
}
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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DE RHAM–WITT COHOMOLOGY FOR A PROPER AND SMOOTH MORPHISM
  • A. Langer, T. Zink
  • Mathematics
    Journal of the Institute of Mathematics of Jussieu
  • 2004
We construct a relative de Rham–Witt complex $W\varOmega^{\cdot}_{X/S}$ for a scheme $X$ over a base scheme $S$. It coincides with the complex defined by Illusie (Annls Sci. Ec. Norm. Super.12
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