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
to the Deligne cohomology spectrum. Secondly, Arakelov motivic cohomology is a generalization of arithmetic
K
-theory and arithmetic Chow groups. Finally, we give a conceptual explanation of the height pairing: it is given by the natural pairing of motivic homology and Arakelov motivic cohomology.