Goncharov's relations in Bloch's higher Chow group CH^3(F,5)
Algebraic Geometry
2009-07-02 v2
Abstract
Using Totaro-Bloch-Kriz's linear fractional cycles Gangl and Muller-Stach recently prove the 5-term relations for the dilogarithm in Bloch's higher Chow group CH^2(F,3) and the Kummer-Spence relations in some group G(F) over an arbitrary field F where G(F) is isomorphic to CH^3(F,5) up to torsions under the Beilinson-Soule vanishing conjecture that CH^2(F,n)=0 for n>3. In this paper we show that Goncharov's 22-term relations for the trilogarithm also hold in G(F).
Keywords
Cite
@article{arxiv.math/0105084,
title = {Goncharov's relations in Bloch's higher Chow group CH^3(F,5)},
author = {Jianqiang Zhao},
journal= {arXiv preprint arXiv:math/0105084},
year = {2009}
}
Comments
16 pages. This is a simplified version