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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, Germany zink@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

Information

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

References

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