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the absolute and relative de rham–witt complexes

Published online by Cambridge University Press:  01 September 2005

lars hesselholt
lars hesselholt
Affiliation:
department of mathematics, massachusetts institute of technology, 77 massachusetts avenue, cambridge, ma 02139-4307, usalarsh@math.mit.edu
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Abstract

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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 x/wn(s) for a smooth family x/s.

Keywords

de rham–witt complexcrystalline cohomologygauss–manin connection11g2511s7014f30
Type
Research Article
Information
Compositio Mathematica , Volume 141 , Issue 5 , September 2005 , pp. 1109 - 1127
Copyright
foundation compositio mathematica 2005