Nagoya Mathematical Journal

Gauß-Manin connection via Witt-differentials

Andreas Langer and Thomas Zink

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Abstract

Let $X/R$ be a smooth scheme over a ring $R$. Consider the category of locally free crystals of finite rank on the situs $\mathop{\mathit{Crys}}(X/W_{t}(R))$. We show that it is equivalent to the category of locally free $W_{t}(\mathcal{O}_{X})$-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.

Article information

Source
Nagoya Math. J., Volume 179 (2005), 1-16.

Dates
First available in Project Euclid: 5 October 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1128518455

Mathematical Reviews number (MathSciNet)
MR2164399

Zentralblatt MATH identifier
1101.14020

Subjects
Primary: 14F30: $p$-adic cohomology, crystalline cohomology 14F40: de Rham cohomology [See also 14C30, 32C35, 32L10]

Citation

Langer, Andreas; Zink, Thomas. Gauß-Manin connection via Witt-differentials. Nagoya Math. J. 179 (2005), 1--16. https://projecteuclid.org/euclid.nmj/1128518455


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References

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