Vol. 1, No. 3, 2016

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Multiplicative differential algebraic $K$-theory and applications

Ulrich Bunke and Georg Tamme

Vol. 1 (2016), No. 3, 227–258

We construct a version of Beilinson’s regulator as a map of sheaves of commutative ring spectra and use it to define a multiplicative variant of differential algebraic K-theory. We use this theory to give an interpretation of Bloch’s construction of K3-classes and the relation with dilogarithms. Furthermore, we provide a relation to Arakelov theory via the arithmetic degree of metrized line bundles, and we give a proof of the formality of the algebraic K-theory of number rings.

regulator, differential algebraic K-theory, Deligne cohomology, Steinberg relation, dilogarithm
Mathematical Subject Classification 2010
Primary: 19F27
Secondary: 33B30
Received: 24 December 2014
Accepted: 30 December 2014
Published: 18 July 2016
Ulrich Bunke
Fakultät für Mathematik
Universität Regensburg
D-93040 Regensburg
Georg Tamme
Fakultät für Mathematik
Universität Regensburg
D-93040 Regensburg