On the de Rham-Witt complex in mixed characteristic

The purpose of this paper is twofold. Firstly, it gives a thorough treatment of the de Rham-Witt complex for Z((p))-algebras, a construction we first considered in [L. Hesselholt, I. Madsen, Ann. of Math. 158 (2003) 1-113]. This complex is the natural generalization to Z((p)) -algebras of the de Rham-Witt complex for F,-algebras of Bloch-Deligne-Illusie [L. Illusie, Ann. Sci. Ecole Norm. Sup. 12 (4) (1979) 501-661] (for p odd). We also give an explicit formula for the de Rham-Witt complex of a polynomial ring in terms of that of the coefficient ring. Secondly, we generalize the main Theorem C of [L. Hesselholt, I. Madsen, Ann. of Math. 158 (2003) 1-113] to smooth algebras over a discrete valuation ring of mixed characteristic (0, p) with perfect residue field and p odd. (C) 2004 Elsevier SAS.