  Let $X$ be a smooth projective $R$-scheme, where $R$ is a smooth
$\Z$-algebra. As constructed by Hesselholt, we have the absolute big de
Rham-Witt complex $\W\Omega^*_X$ of $X$ at our disposal. There is also a
relative version $\W\Omega^*_{X/R}$ with $\W(R)$-linear differential. In this
paper we study the hypercohomology of the relative (big) de Rham-Witt complex
after truncation with finite truncation sets $S$. We show that it is a
projective $\W_S(R)$-module, provided that the de Rham cohomology is a flat
$R$-module. In addition, we establish a Poincar\'e duality theorem.
