A commutative regulator map into Deligne-Beilinson cohomology
Thomas Wei{\ss}schuh
TL;DR
This paper constructs a commutative regulator map from higher Chow groups to Deligne-Beilinson cohomology using a multiplicative Deligne complex, providing an explicit current-based description.
Contribution
It introduces a new commutative version of the regulator map leveraging a multiplicative Deligne complex, enhancing the explicit understanding of the map.
Findings
Provides an explicit current-based description of the regulator map.
Establishes a commutative version of the regulator map.
Connects higher Chow groups with Deligne-Beilinson cohomology more explicitly.
Abstract
In 1986, Spencer Bloch gave an abstract definition of a (regulator) map from higher Chow groups to Deligne-Beilinson cohomology. This map can be defined on the underlying complexes, and Kerr, Lewis and M\"uller-Stach gave an explicit description of this map in terms of currents. Using a multiplicative version of the Deligne complex, we give a commutative version of this map.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Algebra and Geometry · Algebraic structures and combinatorial models