2007/07/12 by Stavros Garoufalidis, Garoufalidis, Stavros
Engineering · Mathematics · #Advanced Combinatorial Mathematics #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #graph theory and CDMA systems #math.AG #math.NT
paper · pdf · doi:10.48550/arxiv.0707.1828
9 pages, 1 figure
openalex publication_date 2007/07/12 · arxiv created 2007/11/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
There are two infinitesimal (i.e., additive) versions of the K-theory of a field F: one was introduced by Cathelineau, which is an F-module, and another one introduced by Bloch-Esnault, which is an F^*-module. Both versions are equipped with a regulator map, when F is the field of complex numbers. In our short paper we will introduce an extended version of Cathelineau's group, and a complex-valued regulator map given by the entropy. We will also give a comparison map between our extended version and Cathelineau's group. Our results were motivated by two unrelated sources: Neumann's work on the extended Bloch group (which is isomorphic to indecomposable K3 of the complex numbers), and the study of singularities of generating series of hypergeometric multisums. Final version.