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

Geisser, Thomas; Hesselholt, Lars

doi:10.1090/S0894-0347-05-00505-9

The de Rham-Witt complex and -adic vanishing cycles

Authors: Thomas Geisser and Lars Hesselholt
Journal: J. Amer. Math. Soc. 19 (2006), 1-36
MSC (2000): Primary 11G25, 11S70; Secondary 14F30, 19D55
DOI: https://doi.org/10.1090/S0894-0347-05-00505-9
Published electronically: September 16, 2005
MathSciNet review: 2169041
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Abstract: We determine the structure of the reduction modulo of the absolute de Rham-Witt complex of a smooth scheme over a discrete valuation ring of mixed characteristic with log-poles along the special fiber and show that the sub-sheaf fixed by the Frobenius map is isomorphic to the sheaf of -adic vanishing cycles. We use this result together with the main results of op. cit. to evaluate the algebraic -theory with finite coefficients of the quotient field of the henselian local ring at a generic point of the special fiber. The result affirms the Lichtenbaum-Quillen conjecture for this field.

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