Torsion in the Crystalline Cohomology of Singular Varieties

This paper discusses some examples showing that the crystalline cohomology of even very mildly singular projective varieties tends to be quite large. In particular, any singular projective variety with at worst ordinary double points has infinitely generated crystalline cohomology in at least two cohomological degrees. These calculations rely critically on comparisons between crystalline and derived de Rham cohomology.

2010 Mathematics Subject Classification: 14F30,14F40

Keywords and Phrases: Crystalline cohomology, derived de Rham cohomology, Cartier isomorphism, Frobenius lifts

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