An extended version of additive K-theory

Abstract

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 $F^{\ast }$-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 $K_3$ of the complex numbers), and the study of singularities of generating series of hypergeometric multisums. Final version.

9 pages, 1 figure

References in corpus (2)

• A dilogarithmic formula for the Cheeger-Chern-Simons class
• An ansatz for the asymptotics of hypergeometric multisums

Cited by in corpus (1)

• An ansatz for the asymptotics of hypergeometric multisums