  We calculate the one-loop divergences for different vector field models in
curved spacetime. We introduce a classification scheme based on their
degeneracy structure, which encompasses the well-known models of the
non-degenerate vector field, the Abelian gauge field and the Proca field. The
renormalization of the generalized Proca model, which has important
applications in cosmology, is more complicated. By extending standard
heat-kernel techniques, we derive a closed form expression for the one-loop
divergences of the generalized Proca model.
