Total p-differentials on schemes over Z/p²

2017/12/27 by Dupuy, Taylor, Katz, Eric, Rabinoff, Joseph +1 · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1712.09487

Abstract

For a scheme X defined over the length 2 p-typical Witt vectors W₂(k) of a characteristic p field, we introduce total p-differentials which interpolate between Frobenius-twisted differentials and Buium's p-differentials. They form a sheaf over the reduction X₀, and behave as if they were the sheaf of differentials of X over a deeper base below W₂(k). This allows us to construct the analogues of Gauss-Manin connections and Kodaira-Spencer classes as in the Katz-Oda formalism. We make connections to Frobenius lifts, Borger-Weiland's biring formalism, and Deligne--Illusie classes.

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• Lazardian Witt vectors

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