Homology of GL_n over algebraically closed fields

Details Homology of GL_n over algebraically closed fields Homology of GL_n over algebraically closed fields

2007-03-12

arxiv.org/abs/math/0703337v1

J. London Math. Soc. 76 (2007), 605-621

Mathematics

K-Theory and Homology

19 pages, Latex

Scientific paper

In this paper we define higher pre-Bloch groups p_n(F) of a field F. When our base field is algebraically closed we study its connection to the homology of the general linear groups with finite coefficient Z/l where l is a positive integer. As a result of our investigation we give a necessary and sufficient condition for the map H_n(GL_{n-1}(F), Z/l) --> H_n(GL_{n}(F), Z/l)$ to be bijective. We prove that this map is bijective for n < 5. We also demonstrate that the divisibility of p_n(C) is equivalent to the validity of the Friedlander-Milnor Isomorphism Conjecture for (n+1)-th homology of GL_n(C).

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