  We extend previous work on antifield dependent local BRST cohomology for
matter coupled gauge theories of Yang-Mills type to the case of gauge groups
that involve free abelian factors. More precisely, we first investigate in a
model independent way how the dynamics enters the computation of the cohomology
for a general class of Lagrangians in general spacetime dimensions. We then
discuss explicit solutions in the case of specific models. Our analysis has
implications for the structure of characteristic cohomology and for consistent
deformations of the classical models, as well as for divergences/counterterms
and for gauge anomalies that may appear during perturbative quantization.
