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arXiv · 1311.1421

Multiplicative differential algebraic K-theory and applications

Ulrich Bunke·Georg Tamme
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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.

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Ulrich Bunke, Georg Tamme. 2015-10-29. Multiplicative differential algebraic K-theory and applications. https://doi.org/10.2140/akt.2016.1.227

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