  We give bounds for exponential sums over curves defined over Galois rings. We
first define summation subsets as the images of lifts of points from affine
opens of the reduced curve, and we give bounds for the degrees of their
coordinate functions. Then we get bounds for exponential sums, extending
results of Kumar et al., Winnie Li over the projective line, and Voloch Walker
over elliptic and $C_{ab}$ curves.
