  We use the theory of canonical models of Shimura varieties to describe the
projective limit of the curves Y(N), all N, and its automorphism group. In
particular we prove that the Galois group of Q(CM) over Q is an extension of a
certain abelian group by a 2-element group, where Q(CM) stands for the the
extension of Q by all the CM-points on all the curves Y(N).
