Low dimensional homology of linear groups over Hensel local rings
Abstract
We prove that if R is a Hensel local ring with infinite residue field k, the natural map Hi(GL(n,R),Z/p) ---> Hi(GL(n,k),Z/p) is an isomorphism for i <=3, p distinct from char(k). This implies rigidity for Hi(GLn), i <=3, which in turn implies the Friedlander-Milnor conjecture in positive characteristic in degrees <=3.
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