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

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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,y∈PF1x,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,y∈PF1x,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.

References

Primary source

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

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