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Poincaré duality for algebraic de rham cohomology

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Abstract.

We discuss in some detail the algebraic notion of De Rham cohomology with compact supports for singular schemes over a field of characteristic zero. We prove Poincaré duality with respect to De Rham homology as defined by Hartshorne [H.75], so providing a generalization of some results of that paper to the non proper case. In order to do this, we work in the setting of the categories introduced by Herrera and Lieberman [HL], and we interpret our cohomology groups as hyperext groups. We exhibit canonical morphisms of ‘‘cospecialization’’ from complex-analytic De Rham (resp. rigid) cohomology groups with compact supports to the algebraic ones. These morphisms, together with the ‘‘specialization’’ morphisms [H.75, IV.1.2] (resp. [BB, 1]) going in the opposite direction, are shown to be compatible with our algebraic Poincaré pairing and the analogous complex-analytic (resp. rigid) one (resp. [B.97, 3.2]).

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Authors and Affiliations

  1. Dept. of Pure and Appl. Mathematics, University of Padova, Via Belzoni, 7, 35131, Padova, Italy

    Francesco Baldassarri, Maurizio Cailotto & Luisa Fiorot

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  1. Francesco Baldassarri
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  2. Maurizio Cailotto
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  3. Luisa Fiorot
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Correspondence to Francesco Baldassarri.

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Mathematics Subject Classification (2000):Primary 14FXX

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Baldassarri, F., Cailotto, M. & Fiorot, L. Poincaré duality for algebraic de rham cohomology. manuscripta math. 114, 61–116 (2004). https://doi.org/10.1007/s00229-004-0448-y

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  • DOI: https://doi.org/10.1007/s00229-004-0448-y

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