We introduce a refinement of the Bloch-Wigner complex of a field F. This refinement is complex of modules over the multiplicative group of the field. Instead of computing K 2 (F) and K ind 3 (F) - as the classical Bloch-Wigner complex does - it calculates the second and third integral homology of SL2 (F). On passing to F × -coinvariants we recover the classical Bloch-Wigner complex. We include the case of finite fields throughout the article
