Adelic resolution and its applications

We discuss a new type of resolutions, called adelic resolutions, for a certain class of abelian sheaves on algebraic varieties. This class includes sheaves of K-groups. Adelic resolutions are multiplicative and contravariant (in contrast with the Gersten resolution). There is an explicit quasiisomorphism between the adelic and Gersten resolutions. In particular, this allows to describe (higher) products on Chow groups and biextensions over Chow groups in terms of the adelic resolution.