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2005 Gauß-Manin connection via Witt-differentials
Andreas Langer, Thomas Zink
Nagoya Math. J. 179: 1-16 (2005).


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.


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Andreas Langer. Thomas Zink. "Gauß-Manin connection via Witt-differentials." Nagoya Math. J. 179 1 - 16, 2005.


Published: 2005
First available in Project Euclid: 5 October 2005

zbMATH: 1101.14020
MathSciNet: MR2164399

Primary: 14F30 , 14F40

Rights: Copyright © 2005 Editorial Board, Nagoya Mathematical Journal

Vol.179 • 2005
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