Low dimensional homology of linear groups over Hensel local rings

Details Low dimensional homology of linear groups over Hensel local rings Low dimensional homology of linear groups over Hensel local rings

1998-01-21

arxiv.org/abs/math/9801098v1

Mathematics

K-Theory and Homology

15 pages

Scientific paper

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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