Bivariant Chow groups and the topology of envelopes

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