Bivariant Chow groups and the topology of envelopes

Let K be an algebraically closed field and let Sch K denote the category of schemes over K. Our objective is to extend the operational Chow theory to presheaves (of sets) on Sch K . More generally, we introduce bivariant Chow groups CH p ( f : F → G ) , p ∈ Z for a representable morphism of presheaves on Sch K . These are then studied with the help of the topology of envelopes on Sch K .