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arXiv · 1204.5709

The third homology of SL_2 of fields with discrete valuation

Kevin Hutchinson
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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.

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Kevin Hutchinson. 2012-04-25. The third homology of SL_2 of fields with discrete valuation. https://arxiv.org/abs/1204.5709

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