Arakelov motivic cohomology II

Scholbach, Jakob

doi:10.1090/jag/647

Author: Jakob Scholbach
Journal: J. Algebraic Geom. 24 (2015), 755-786
DOI: https://doi.org/10.1090/jag/647
Published electronically: June 18, 2015
MathSciNet review: 3383603
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Abstract | References | Additional Information

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 $\operatorname {BGL}$ to the Deligne cohomology spectrum. Secondly, Arakelov motivic cohomology is a generalization of arithmetic $K$-theory and arithmetic Chow groups. For example, this implies a decomposition of higher arithmetic $K$-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.

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Additional Information

Jakob Scholbach
Affiliation: Universität Münster, Mathematisches Institut, Einsteinstrasse 62, D-48149 Münster, Germany
Email: jakob.scholbach@uni-muenster.de

Received by editor(s): October 10, 2012
Received by editor(s) in revised form: June 26, 2013
Published electronically: June 18, 2015
Additional Notes: The author would like to thank Andreas Holmstrom for the collaboration leading to part I of this project
Article copyright: © Copyright 2015 University Press, Inc.