Total $p$differentials on schemes over $Z/p^2$
Abstract
For a scheme $X$ defined over the length $2$ $p$typical Witt vectors $W_2(k)$ of a characteristic $p$ field, we introduce total $p$differentials which interpolate between Frobeniustwisted differentials and Buium's $p$differentials. They form a sheaf over the reduction $X_0$, and behave as if they were the sheaf of differentials of $X$ over a deeper base below $W_2(k)$. This allows us to construct the analogues of GaussManin connections and KodairaSpencer classes as in the KatzOda formalism. We make connections to Frobenius lifts, BorgerWeiland's biring formalism, and DeligneIllusie classes.
 Publication:

arXiv eprints
 Pub Date:
 December 2017
 DOI:
 10.48550/arXiv.1712.09487
 arXiv:
 arXiv:1712.09487
 Bibcode:
 2017arXiv171209487D
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Number Theory
 EPrint:
 11 pages