  We state and investigate an integral analogue of the Andr\'e-Oort conjecture
(in integral models of Shimura varieties). We establish an instance of this
conjecture: the case of a modular curve, as a scheme over Z. It is a scheme of
dimension two and, already in this case, our conjecture is highly non-trivial.
Our approach relies on equidistribution estimates related to subconvexity in
analytic number theory and our result is unconditional.
