2019/04/10 by Sı̇nan Ünver, Sinan Unver, Unver, Sinan · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG
paper · pdf · doi:10.48550/arxiv.1904.05409
arxiv created 2019/04/10 · openalex publication_date 2019/04/10 · arxiv updated 2019/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Borel's construction of the regulator gives an injective map from the algebraic K-groups of a number field to its Deligne-Beilinson cohomology groups. This has many interesting arithmetic and geometric consequences. The formula for the regulator is expressed in terms of the classical polyogarithm functions. In this paper, we give a survey of the additive dilogarithm and the several different versions of the weight two regulator in the infinitesimal setting. We follow a historical approach which we hope will provide motivation for the definitions and the constructions.