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Pré-Publication, Document De Travail Année : 2021

The Hodge realization functor on the derived category of relative motives

Résumé

We give, for a complex algebraic variety S, a Hodge realization functor F Hdg S from the (un-bounded) derived category of constructible motives DAc(S) over S to the (undounded) derived category D(M HM (S)) of algebraic mixed Hodge modules over S. Moreover, for f : T → S a morphism of complex quasi-projective algebraic varieties, F Hdg − commutes with the four operations f * , f * , f ! , f ! on DAc(−) and D(M HM (−)), making in particular the Hodge realization functor a morphism of 2-functor on the category of complex quasi-projective algebraic varieties which for a given S sends DAc(S) to D(M HM (S)), moreover F Hdg S commutes with tensor product. We also give an algebraic and analytic Gauss-Manin realization functor from which we obtain a base change theorem for algebraic De Rham cohomology and for all smooth morphisms a relative version of the comparaison theorem of Grothendieck between the algebraic De Rahm cohomology and the analytic De Rahm cohomology.
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Dates et versions

hal-02888285 , version 1 (02-07-2020)
hal-02888285 , version 2 (05-07-2020)
hal-02888285 , version 3 (28-08-2020)
hal-02888285 , version 4 (20-11-2020)
hal-02888285 , version 5 (03-02-2021)
hal-02888285 , version 6 (24-02-2021)
hal-02888285 , version 7 (03-03-2021)
hal-02888285 , version 8 (18-03-2021)
hal-02888285 , version 9 (22-03-2021)
hal-02888285 , version 10 (17-01-2022)
hal-02888285 , version 11 (24-01-2022)

Identifiants

  • HAL Id : hal-02888285 , version 7

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Johann Bouali. The Hodge realization functor on the derived category of relative motives. 2021. ⟨hal-02888285v7⟩
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