Neumann's strong conjecture on Bloch groups of number fields

Let FCF\subset\mathbb C be a concrete number field which is not contained in R\mathbb R. Let B(F)\mathcal B(F) be the Bloch group of FF, and call a hyperbolic 33-manifold admissible over FF when its invariant trace field is contained in FF. Neumann's strong conjecture. The Bloch group B(F)\mathcal B(F) is generated integrally modulo torsion by admissible hyperbolic 33-manifolds. The conjecture refines generation over C\mathbb C to each non-real concrete number field; the source gives no resolution.

Sources & referencesView supporting material

Primary source

Stavros Garoufalidis, Dylan P. Thurston and Christian K. Zickert, “The complex volume of SL(n,C)-representations of 3-manifolds”, arXiv:1111.2828 (2013).

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