The third homology of SL₂ of fields with discrete valuation

2012/04/25 by Hutchinson, Kevin
#19D99 #20J05 #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1204.5709

Abstract

For a field F with discrete valuation and residue field k we relate the third homology of SL₂(F) with half-integral coefficients to the third homology of SL₂(k) and a certain refined scissors congruence group of k. As an application, we obtain explicit calculations of the third homology of SL₂ 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.

Related

• Low-dimensional Homology of SL₂(k[t,1/t])
• Third homology of SL₂ over Number fields: The norm-Euclidean quadratic imaginary case
• The homology of SL₂ of discrete valuation rings
• The third homology of the special linear group of a field
• The third homology of SL₂ of local rings