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arXiv · 1107.0264

A Bloch-Wigner complex for SL_2

Kevin Hutchinson
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Abstract

We introduce a refinement of the Bloch-Wigner complex of a field F. This is a complex of modules over the multiplicative group of the field. Instead of computing K_2 and indecomposable K_3 - as the classical Bloch-Wigner complex does - it calculates the second and third integral homology of SL_2 of the field. On passing to coinvariants for the action of the multiplicative group we recover the classical Bloch-Wigner complex. The case of finite fields is included throughout the article.

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Kevin Hutchinson. 2011-07-01. A Bloch-Wigner complex for SL_2. https://arxiv.org/abs/1107.0264

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