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

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

2011-01-17

arxiv.org/abs/1101.3279v4

Mathematics

K-Theory and Homology

35 pages. Minor changes to the exposition

Scientific paper

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.

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