A refined Bloch group and the third homology of SL_2 of a field

Abstract

We use the properties of the refined Bloch group of a field to prove that H_3 of SL_2 of a global field is never finitely generated, and to calculate - up to some 2-torsion - H_3 of SL_2 of local fields with finite residue field of odd characteristic. We also give lower bounds for the 3-torsion in the H_3 of SL_2 of rings of S-integers.

42 pages. Details added and exposition improved thanks to referee. To appear, J. Pure Applied Algebra

References in corpus (3)

• The integral homology of $PS{L}_2$ of imaginary quadratic integers with non-trivial class group
• Homology and K-theory of the Bianchi groups
• A Bloch-Wigner complex for SL_2

Cited by in corpus (2)

• The third homology of SL_2 of fields with discrete valuation
• On third homology of SL_2 and weak homotopy invariance