### 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>