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Gauss-Manin connection via Witt-Differentials

Published online by Cambridge University Press:  11 January 2016

Andreas Langer  and
Thomas Zink
Andreas Langer
Affiliation:
Mathematics, University of Exeter, Exeter, EX4 4QE Devon, UK, a.langer@ex.ac.uk
Thomas Zink
Affiliation:
Fakultät für Mathematik Universität Bielefeld, Postfach 100131 D-33501 Bielefeld, Germanyzink@mathematik.uni-bielefeld.de
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Abstract

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Let X/R be a smooth scheme over a ring R. Consider the category of locally free crystals of finite rank on the situs Crys(X/Wt(R)). We show that it is equivalent to the category of locally free -modules of finite rank endowed with a nilpotent, integrable de Rham-Witt connection. In the case where R is a perfect field this was shown by Etesse [E] and Bloch [Bl]. We use the result for a construction of the Gauß-Manin connection as a de Rham-Witt connection.

Keywords

14F3014F40
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 179 , 2005 , pp. 1 - 16
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2005

References

[B] Berthelot, P., Cohomologie cristalline des schémas de charactéristique p > 0, Springer LNM 407, 1974.Google Scholar
[B-O] Berthelot, P. and Ogus, A., Notes on crystalline cohomology, Princeton, 1978.Google Scholar
[Bl] Bloch, S., Crystals and de Rham-Witt connections, J. Inst. Math. Jussieu, 3 (2004), no. 3, 315–326.Google Scholar
[E] Etesse, J.-Y., Complexe de De Rham-Witt à coefficients dans un crystal, Comp. Math., 66 (1988), 57–120.Google Scholar
[H] Hartshorne, R., Residues and Duality, Springer LNM 20, 1966.Google Scholar
[K] Katz, N., Nilpotent connections and the monodromy theorem: Applications of a result of Turritin, IHES Publ. Math. No.3 (1970).CrossRefGoogle Scholar
[K-O] Katz, N. and Oda, T., On the differentiation of de Rham cohomology classes with respect to parameters, J. Math. Kyoto Univ., 8-2 (1968), 199–213.Google Scholar
[L-Z] Langer, A. and Zink, Th., De Rham-Witt cohomology for a proper and smooth morphism, preprint (2001). http://www.mathematik.uni-bielefeld.de/~zink.Google Scholar