Local BRST cohomology and covariance

The paper provides a framework for a systematic analysis of the local BRST cohomology in a large class of gauge theories. The approach is based on the cohomology of s + d in the jet space of fields and antifields, s and d bring the BRST operator and exterior derivative respectively. It relates the BRST cohomology to an underlying gauge covariant algebra and reduces its computation to a compactly formulated problem involving only suitably defined generalized connections and tensor fields. The latter are shown to provide the building blocks of physically relevant quantities such as gauge invariant actions, Noether currents and gauge anomalies, as well as of the equations of motion.