  We prove two types of results. First we develop the decoupling theory for
hypersurfaces with nonzero Gaussian curvature, which extends our earlier work
from \cite{BD3}. As a consequence of this we obtain sharp (up to $\epsilon$
losses) Strichartz estimates for the hyperbolic Schr\"odinger equation on the
torus.
  Our second main result is an $l^2$ decoupling for non degenerate curves which
has implications for Vinogradov's mean value theorem.
