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arXiv:1311.1421 [math.NT]AbstractReferencesReviewsResources

Multiplicative differential algebraic K-theory and applications

Ulrich Bunke, Georg Tamme

Published 2013-11-06, updated 2015-10-29Version 3

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 K_3-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.

Comments: v1:28 pages, v2:revised version, v3:references updated, changed numbering to match published version. To appear in Annals of K-Theory
Categories: math.NT, math.AG, math.KT
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