Arakelov motivic cohomology II

Abstract

We show that the constructions done in part I generalize their classical counterparts: firstly, the classical Beilinson regulator is induced by the abstract Chern class map from BGL \operatorname {BGL} to the Deligne cohomology spectrum. Secondly, Arakelov motivic cohomology is a generalization of arithmetic K K -theory and arithmetic Chow groups. For example, this implies a decomposition of higher arithmetic K K -groups in its Adams eigenspaces. Finally, we give a conceptual explanation of the height pairing: it is the natural pairing of motivic homology and Arakelov motivic cohomology.