Vol. 1, No. 3, 2016

Download this article
Download this article For screen
For printing
Recent Issues
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the Journal
Subscriptions
Editorial Board
Ethics Statement
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
Author Index
To Appear
Contacts
ISSN: 2379-1691 (e-only)
ISSN: 2379-1683 (print)
Other MSP Journals
Multiplicative differential algebraic $K$-theory and applications

Ulrich Bunke and Georg Tamme

Vol. 1 (2016), No. 3, 227–258
Abstract

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.

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