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Exotic Torsion, Frobenius Splitting and the Slope Spectral Sequence

  Published:2007-12-01
 Printed: Dec 2007
  • Kirti Joshi
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Abstract

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.
Keywords: threefolds, Frobenius splitting, Hodge--Witt, crystalline cohomology, slope spectral sequence, exotic torsion threefolds, Frobenius splitting, Hodge--Witt, crystalline cohomology, slope spectral sequence, exotic torsion
MSC Classifications: 14F30, 14J30 show english descriptions $p$-adic cohomology, crystalline cohomology
$3$-folds [See also 32Q25]
14F30 - $p$-adic cohomology, crystalline cohomology
14J30 - $3$-folds [See also 32Q25]
 

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