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# Exotic Torsion, Frobenius Splitting and the Slope Spectral Sequence

In this paper we show that any Frobenius split, smooth, projective threefold over a perfect field of characteristic $p>0$ is Hodge--Witt. This is proved by generalizing to the case of threefolds a well-known criterion due to N.~Nygaard for surfaces to be Hodge-Witt. We also show that the second crystalline cohomology of any smooth, projective Frobenius split variety does not have any exotic torsion. In the last two sections we include some applications.
 MSC Classifications: 14F30 - $p$-adic cohomology, crystalline cohomology 14J30 - $3$-folds [See also 32Q25]