### The absolute and relative de Rham-Witt complexes

We compare the absolute and relative de Rham-Witt complexes considered
by the author and Madsen and by Langer and Zink, which both generalize
the classical de Rham-Witt complex of Bloch, Deligne, and Illusie from
**F**_{p}-schemes to **Z**_{(p)}-schemes. From
this comparison, we derive a Gauss-Manin connection on the crystalline
cohomology of X/W_{n}(S) for a smooth family X/S. The
comparison result is based on a formula that expresses the absolute de
Rham-Witt complex of a polynomial algebra in a finite number over a
variables in terms of the absolute de Rham-Witt complex of the ring of
coefficients. The formula in the one-variable case was proved in
earlier joint work with Ib Madsen, and the analogous result for the
relative de Rham-Witt complex was proved by Langer and Zink.

Lars Hesselholt
<larsh@math.nagoya-u.ac.jp>