Low dimensional homology of linear groups over Hensel local rings

1998/01/21 by Kevin P. Knudson, Knudson, Kevin P.
Mathematics · #20G10 #FOS: Mathematics #Group Theory (math.GR) #K-Theory and Homology (math.KT) #math.GR #math.KT #msc:20G10

paper · pdf · doi:10.48550/arxiv.math/9801098

15 pages

arxiv created 1998/01/21 · arxiv updated 2009/11/30

Abstract

We prove that if R is a Hensel local ring with infinite residue field k, the natural map H_i(GL(n,R),Z/p) ---> H_i(GL(n,k),Z/p) is an isomorphism for i <=3, p distinct from char(k). This implies rigidity for H_i(GL_n), i <=3, which in turn implies the Friedlander-Milnor conjecture in positive characteristic in degrees <=3.

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