Multiplicative differential algebraic K-theory and applications
arXiv:1311.1421 · 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 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.
v1:28 pages, v2:revised version, v3:references updated, changed numbering to match published version. To appear in Annals of K-Theory