The third homology of SL₂ of fields with discrete valuation

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• 作者：Kevin Hutchinson ^{kevin.hutchinson@ucd.ie}
• 关键词：19D99 ; 20J05 ; 20G10
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2017
• 出版时间：May 2017
• 年：2017
• 卷：221
• 期：5
• 页码：1076-1111
• 全文大小：610 K
• 卷排序：221

文摘

For a field F with discrete valuation and residue field k   we relate the third homology of SL2(F)SL2(F) with half-integral coefficients to the third homology of SL2(k)SL2(k) and a certain refined scissors congruence group of k  . As an application, we obtain explicit calculations of the third homology of SL2SL2 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.