Goncharov's five-term generation conjecture for the Bloch relations

Let FF be a field and let R2(F)R_2(F) be the subgroup of the relevant free abelian group generated by functional relations in weight two. For x,yPF1x,y\in P^1_F, write FT[x,y]FT[x,y] for the five-term relation, using the conventions 0/0=10/0=1 and 0/=00/\infty=0, among others. Goncharov's five-term generation conjecture. The group R2(F)R_2(F) is the subgroup generated by the elements FT[x,y]FT[x,y], where x,yPF1x,y\in P^1_F. This would identify all weight-two relations with the classical five-term relations and yield the expected comparison with the classical Bloch group, modulo the torsion qualifications stated in the paper.

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Primary source

Christian K. Zickert, “Holomorphic polylogarithms and Bloch complexes”, arXiv:1902.03971 (2023).

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