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Gauss-Manin connection via Witt-Differentials
Published online by Cambridge University Press: 11 January 2016
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 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.
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- Copyright © Editorial Board of Nagoya Mathematical Journal 2005
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