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An extended version of additive K-theory

Published online by Cambridge University Press:  14 November 2008

Stavros Garoufalidis
Stavros Garoufalidis
Affiliation:
[email protected]://www.math.gatech.edu/~stavrosSchool of MathematicsGeorgia Institute of TechnologyAtlanta, GA 30332-0160USA
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Abstract

There are two infinitesimal (i.e., additive) versions of the K-theory of a field F: one introduced by Cathelineau, which is an F-module, and the other 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.

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.

Keywords

infinitesimal K-theoryadditive K-theoryregulatorsentropy4-term relationStirling formulabinomial coefficientsinfinitesimal polylogarithmsBloch groupextended Bloch group
Type
Research Article
Information
Journal of K-Theory , Volume 4 , Issue 2 , October 2009 , pp. 391 - 403
Copyright
Copyright © ISOPP 2009

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