Abstract: | In this paper we define higher pre-Bloch groups n(F) of a fieldF. When the base field is algebraically closed, we study itsconnection to the homology of the general linear groups withcoefficients in /l , where l is a positive integer. As a resultof our investigation we give a necessary and sufficient conditionfor the natural map Hn(GLn–1(F), /l ) Hn(GLn(F), /l )to be bijective. We prove that this map is bijective for n4.We also demonstrate that a certain property of n() is equivalentto the validity of the Friedlander–Milnor isomorphismconjecture for (n+1)th homology of GLn(). |