Homology of GL_n over algebraically closed fields
K-Theory and Homology
2008-04-18 v1
Abstract
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).
Keywords
Cite
@article{arxiv.math/0703337,
title = {Homology of GL_n over algebraically closed fields},
author = {Behrooz Mirzaii},
journal= {arXiv preprint arXiv:math/0703337},
year = {2008}
}
Comments
19 pages, Latex