Examples of non-algebraic classes in the Brown-Peterson tower

Abstract

For every n≥0 , we construct classes in the Brown–Peterson cohomology BP⟨n⟩ of smooth projective complex algebraic varieties which are not in the image of the cycle map from the corresponding motivic Brown–Peterson cohomology. This generalizes the examples of Atiyah and Hirzebruch to all finite levels in the Brown–Peterson tower.