TL;DR
This paper extends classical concepts like the Beilinson regulator and arithmetic K-theory within the framework of Arakelov motivic cohomology, providing a conceptual understanding of the height pairing.
Contribution
It generalizes classical constructions to Arakelov motivic cohomology and offers a conceptual explanation for the height pairing.
Findings
Classical Beilinson regulator is induced by an abstract Chern class map.
Arakelov motivic cohomology generalizes arithmetic K-theory and Chow groups.
Height pairing is explained as a natural pairing of motivic homology and Arakelov motivic cohomology.
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 to the Deligne cohomology spectrum. Secondly, Arakelov motivic cohomology is a generalization of arithmetic -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.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory · Advanced Algebra and Geometry