  We prove that the cohomology groups of an etale Q_p-local system on a smooth
proper rigid analytic space are finite-dimensional Q_p-vector spaces, provided
that the base field is either a finite extension of Q_p or an algebraically
closed nonarchimedean field containing Q_p. This result manifests as a special
case of a more general finiteness result for the higher direct images of a
relative (phi, Gamma)-module along a smooth proper morphism of rigid analytic
spaces over a mixed-characterstic nonarchimedean field.
