English

A survey of the additive dilogarithm

Algebraic Geometry 2019-04-12 v1

Abstract

Borel's construction of the regulator gives an injective map from the algebraic KK-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.

Cite

@article{arxiv.1904.05409,
  title  = {A survey of the additive dilogarithm},
  author = {Sinan Unver},
  journal= {arXiv preprint arXiv:1904.05409},
  year   = {2019}
}
R2 v1 2026-06-23T08:36:00.073Z