2012/05/17 by Scholbach, Jakob
#14F35 #14G40 #19E08 #Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT) #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1205.3890
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.