Low dimensional homology of linear groups over Hensel local rings

الأصل · EN

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.