Ultraproducts and the discrete cohomology of algebraic groups, by J.F. Jardine

This paper gives a reformulation of the generalized isomorphism conjecture of Friedlander and Milnor on the discrete cohomology of special linear groups, in terms of ultraproducts of classifying spaces of special linear groups over algebraic closures of finite fields. The classical ultraproduct construction is reinterpreted in terms of various stalks of direct image sheaves on a topos associated to the category of subsets of a fixed index set equipped with topology of finite coverings, so that the problem underlying the Friedlander-Milnor conjecture is a question of whether or not a particular map of simplicial objects in this topos is a homology isomorphism. The conjecture is a consequence of a statement about ultraproducts of classifying spaces which involve only finite fields.

The paper is no longer kept here, as it has been published: J.F. Jardine, "Ultraproducts and the discrete cohomology of algebraic groups", Algebraic K-Theory, Fields Institute Communications, Vol. 16, AMS (1997), 111-130.


J.F. Jardine <jardine@uwo.ca>