Open Access
Translator Disclaimer
2016 Multiplicative differential algebraic $K$-theory and applications
Ulrich Bunke, Georg Tamme
Ann. K-Theory 1(3): 227-258 (2016). DOI: 10.2140/akt.2016.1.227

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.

Citation

Download Citation

Ulrich Bunke. Georg Tamme. "Multiplicative differential algebraic $K$-theory and applications." Ann. K-Theory 1 (3) 227 - 258, 2016. https://doi.org/10.2140/akt.2016.1.227

Information

Received: 24 December 2014; Accepted: 30 December 2014; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1375.19009
MathSciNet: MR3529091
Digital Object Identifier: 10.2140/akt.2016.1.227

Subjects:
Primary: 19F27
Secondary: 33B30

Keywords: Deligne cohomology , differential algebraic K-theory , dilogarithm , regulator , Steinberg relation

Rights: Copyright © 2016 Mathematical Sciences Publishers

JOURNAL ARTICLE
32 PAGES


SHARE
Vol.1 • No. 3 • 2016
MSP
Back to Top