Torsion in the crystalline cohomology of singular varieties
Copyright policy )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.
Mathematics - Number Theory, \(p\)-adic cohomology, crystalline cohomology, crystalline cohomology, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Frobenius lifts, cartier isomorphism, Mathematics - Algebraic Geometry, FOS: Mathematics, Number Theory (math.NT), derived de Rham cohomology, Algebraic Geometry (math.AG), de Rham cohomology and algebraic geometry
Mathematics - Number Theory, \(p\)-adic cohomology, crystalline cohomology, crystalline cohomology, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Frobenius lifts, cartier isomorphism, Mathematics - Algebraic Geometry, FOS: Mathematics, Number Theory (math.NT), derived de Rham cohomology, Algebraic Geometry (math.AG), de Rham cohomology and algebraic geometry
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