The third homology of SL_2 of fields with discrete valuation

Abstract

For a field F with discrete valuation and residue field $k$ we relate the third homology of SL_2(F) with half-integral coefficients to the third homology of SL_2(k) and a certain refined scissors congruence group of k. As an application, we obtain explicit calculations of the third homology of SL_2 of certain higher-dimensional local fields in terms of scissors congruence groups, in the sense of Dupont and Sah, of the residue fields of the associated valuations.

40 pages (including Appendix)

References in corpus (1)

• The third homology of SL_2 of local rings

Cited by in corpus (2)

• The third homology of SL_2 of local rings
• On third homology of SL_2 and weak homotopy invariance