Topological Models for Arithmetic
By: William G. Dwyer and Eric M. Friedlander
Abstract. We find explicit models for the etale topological type of certain
arithmetic rings A, and in some cases use these models to compute
the l-adic topological K-theory of A.
Through a comparison map, this
gives information about the algebraic K-theory of A.
For example, we
are able to compute the mod l cohomology of certain "unstable"
topological K-theory spaces and verify that it injects into the
cohomology
of the corresponding unstable algebraic K-theory spaces. This gives an
explicit lower bound for H*(GL(n, A); Z=l): In some cases we also find
explicit geometric or cohomological reformulations of the Lichtenbaum-
Quillen conjectures.
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