(Co)homology of abelian groups with (co)invariant coefficients modules

Details (Co)homology of abelian groups with (co)invariant coefficients modules (Co)homology of abelian groups with (co)invariant coefficients modules

2012-04-08

arxiv.org/abs/1204.1723v1

Mathematics

K-Theory and Homology

8 pages, Latex

Scientific paper

Let A be an abelian group, B a subgroup of A and let M be an A-module. We
show that if A/B is finite, l-torsion and M is a Z[1/l]-module, then the
natural maps H_n(A, M_B)--> H_n(A,M_A), H^n(A, M^A)--> H^n(A,M^B) are
isomorphism. We use these isomorphisms to study the homology and cohomology of
special linear groups.

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