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

General solutions of the Wess-Zumino consistency condition for the Weyl anomalies