Algebraic determination of covariant anomalies and Schwinger terms

Inclusion of the anti-ghost field in the BRST algebra allows us to derive simultaneously consistent and covariant anomalies and Schwinger terms (as well as Bardeen-Zumino counterterms) by transgression form a Chern-Simons form. Our method which uses the natural variables of the gauged BRST symmetry encompasses all polynomials and descent equations of a previously proposed approach which relies on various homotopy operators. In conclusion, both approaches are generalized to gravitational theories. (orig.)