  We study conformal actions of connected nilpotent Lie groups on compact
pseudo-Riemannian manifolds. We prove that if a type-(p,q) compact manifold M
supports a conformal action of a connected nilpotent group H, then the degree
of nilpotence of H is at most 2p+1, assuming p <= q; further, if this maximal
degree is attained, then M is conformally equivalent to the universal
type-(p,q), compact, conformally flat space, up to finite covers. The proofs
make use of the canonical Cartan geometry associated to a pseudo-Riemannian
conformal structure.
