Linear group homology properties of the inclusion of a ring of integers into a number field, by Dominique Arlettaz and Piotr Zelewski

This paper will appear in the Proceedings of the 1994 Barcelona Conference on Algebraic Topology. The inclusion of a ring of integers O into its number field F induces a homomorphism f from the n-th homology group (with integral coefficients) of the infinite special linear group over O to the n-th homology group of the infinite special linear group over F. We prove the following two theorems for any prime number p and any dimension n which is small enough (depending on p): a) the homomorphism f is injective after localization at p; b) all p-torsion divisible classes in the n-th homology group of SL(F) belong to the image of f.

This paper has been published in "Algebraic Topoology: New Trends in Localization and Periodicity", Proceedings of the 1994 Barcelona Conference on Algebraic Topology, Progress in Mathematics 136 (1996) 23-31.


Dominique Arlettaz <dominique.arlettaz@ima.unil.ch>
Piotr Zelewski <piotr@icarus.math.mcmaster.ca>