Arithmetic subgroups whose representations all map into GL_n(Z) Dave Witte Morris University of Lethbridge Suppose Γ is an arithmetic subgroup of a semisimple Lie group G. For any finite-dimensional representation ρ:G→GLn(R), a classical paper of J. Tits determines whether ρ(Γ) is conjugate to a subgroup of GLn(Z). Combining this with a well-known surjectivity result in Galois cohomology provides a short proof of the known fact that every G has an arithmetic subgroup Γ, such that the containment is true for \emph{every} representation ρ. We will not assume the audience is acquainted with Galois cohomology or the theorem of Tits.