The de Rham-Witt and Zp-cohomologies of an algebraic variety

We prove that, for a smooth complete variety X over a perfect field,Hi(X,Zp(r))≅HomDcb(R)(1,RΓ(WΩX
- )(r)[i]),where Hi(X,Zp(r))=lim←nHi-r(Xet,νn(r)) (Amer. J. Math. 108 (2) (1986) 297-360), WΩX
- is the de Rham-Witt complex on X (Ann. Scient. Ec. Num. Sup. 12 (1979b) 501-661), and Dcb(R) is the triangulated category of coherent complexes over the Raynaud ring (Inst. Hautes. Etuder Sci. Publ. Math. 57 (1983) 73-212).