  We prove the Noether-Lefschetz conjecture on the moduli space of
quasi-polarized K3 surfaces. This is deduced as a particular case of a general
theorem that states that low degree cohomology classes of arithmetic manifolds
of orthogonal type are dual to the classes of special cycles, i.e.
sub-arithmetic manifolds of the same type. For compact manifolds this was
proved in \cite{BMM11}, here we extend the results of \cite{BMM11} to
non-compact manifolds. This allows us to apply our results to the moduli spaces
of quasi-polarized K3 surfaces.
