The absolute and relative de Rham-Witt complexes

Abstract

we compare the absolute and relative de rham-witt complexes considered by hesselholt and madsen (ann. sci. école norm. sup. 37 (2004), 1-43; ann. of math. (2) 158 (2003), 1-113) and by langer and zink (j. inst. math. jussieu 3 (2004), 231-314), which both generalize the classical de rham-witt complex of bloch, deligne, and illusie (ann. sci. école norm. sup. (4) 12 (1979), 501-661) from $\mathbb{f}_p$-schemes to $\mathbb{z}_{(p)} $-schemes. from this comparison, we derive a gauss-manin connection on the crystalline cohomology of xwn(s) for a smooth family xs. © Foundation Compositio Mathematica 2005.