  The general solutions of the Wess-Zumino consistency condition for the
conformal (or Weyl, or trace) anomalies are derived. The solutions are
obtained, in arbitrary dimensions, by explicitly computing the cohomology of
the corresponding Becchi-Rouet-Stora-Tyutin differential in the space of
integrated local functions at ghost number unity. This provides a purely
algebraic, regularization-independent classification of the Weyl anomalies in
arbitrary dimensions. The so-called type-A anomaly is shown to satisfy a
non-trivial descent of equations, similarly to the non-Abelian chiral anomaly
in Yang-Mills theory.
