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Exotic Torsion, Frobenius Splitting and the Slope Spectral Sequence

Published online by Cambridge University Press:  20 November 2018

Kirti Joshi
Kirti Joshi*
Affiliation:
Mathematics Department, University of Arizona, 617 N. Santa Rita, Tucson, AZ 85721-0089, U.S.A. e-mail: kirti@math.arizona.edu
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Abstract

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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 $\text{N}$. 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

14F3014J30threefoldsFrobenius splittingHodge–Wittcrystalline cohomologyslope spectral sequenceexotic torsion
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 50 , Issue 4 , 01 December 2007 , pp. 567 - 578
Copyright
Copyright © Canadian Mathematical Society 2007

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