  We study the coupling of a 2+1 dimensional non-relativistic spin 1/2 fermion
to a curved Newton-Cartan geometry, using null reduction from an
extra-dimensional relativistic Dirac action in curved spacetime. We analyze
Weyl invariance in detail: we show that at the classical level it is preserved
in an arbitrary curved background, whereas at the quantum level it is broken by
anomalies. We compute the trace anomaly using the Heat Kernel method and we
show that the anomaly coefficients a, c are proportional to the relativistic
ones for a Dirac fermion in 3+1 dimensions. As for the previously studied
scalar case, these coefficents are proportional to 1/m, where m is the
non-relativistic mass of the particle.
