Abstract:Abstract Global intersection theories for smooth algebraic varieties via products in appropriate Poincaré duality theories are obtained. We assume given a (twisted) cohomology theory H * having a cup ...Abstract Global intersection theories for smooth algebraic varieties via products in appropriate Poincaré duality theories are obtained. We assume given a (twisted) cohomology theory H * having a cup product structure and we consider the ℋ︁‐ cohomology functor X ↝ H # Zar ( X, ℋ︁* ) where ℋ︁* is the Zariski sheaf associated to H *. We show that the ℋ︁‐ cohomology rings generalize the classical “intersection rings” obtained via rational or algebraic equivalences. Several basic properties e. g. Gysin maps, projection formula and projective bundle decomposition, of ℋ︁‐ cohomology are obtained. We therefore obtain, for X smooth, Chern classes c P, i : K i ( X )→ H p‐i ( X,ℋ︁ p ) from the Quillen K‐ theory to ℋ︁‐ cohomologies according to Gillet and Grothendieck. We finally obtain the “blow‐up formula” magnified image where X′ is the blow–up of X smooth, along a closed smooth subset Z of pure codimension c. Singular cohomology of associated analityc space, étale cohomology, de Rham and Deligne–Beilinson cohomologies are examples for this setting.Read More
Publication Year: 1997
Publication Date: 1997-01-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 11
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