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arXiv · 1904.05409

A survey of the additive dilogarithm

Sinan Unver
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Abstract

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.

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Sinan Unver. 2019-04-10. A survey of the additive dilogarithm. https://arxiv.org/abs/1904.05409

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