2013/11/30 by Ulrich Bunke, Georg Tamme
Computer Science · Mathematics · #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic number #Differential (mechanical device) #Formality #Homotopy and Cohomology in Algebraic Topology #Line (geometry) #Multiplicative function #Polynomial and algebraic computation #Relation (database) #Ring (chemistry) #math.AG #math.KT #math.NT
paper · pdf · doi:10.2140/akt.2016.1.227
published as Ann. K-Theory 1 (2016), No. 3, 227-258 · v1:28 pages, v2:revised version, v3:references updated, changed numbering to match published version. To appear in Annals of K-Theory
arxiv created 2015/10/29 · openalex created_date 2016/06/24 · openalex publication_date 2016/07/18 · arxiv updated 2016/07/28 · openalex updated_date 2026/08/05
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 [math] -theory. We use this theory to give an interpretation of Bloch’s construction of [math] -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 [math] -theory of number rings.