Presheaf with transfers

rdf:langString Presheaf with transfers

rdf:langString In algebraic geometry, a presheaf with transfers is, roughly, a presheaf that, like cohomology theory, comes with pushforwards, “transfer” maps. Precisely, it is, by definition, a contravariant additive functor from the category of finite correspondences (defined below) to the category of abelian groups (in category theory, “presheaf” is another term for a contravariant functor). When a presheaf F with transfers is restricted to the subcategory of smooth separated schemes, it can be viewed as a presheaf on the category with extra maps , not coming from morphisms of schemes but also from finite correspondences from X to Y A presheaf F with transfers is said to be -homotopy invariant if for every X. For example, Chow groups as well as motivic cohomology groups form presheaves with transfers.