Gereon Quick: Examples of non-algebraic classes in the Brown-Peterson tower

Abstract: It is a classical problem in algebraic geometry to decide whether a class in the singular cohomology of a smooth complex variety X is algebraic, that is if it can be realized as the fundamental class of an algebraic subvariety of X. One can ask a similar question for motivic spectra. Given a motivic spectrum E, which classes in the topological E-cohomology of X come from motivic classes. I will discuss this question and examples of non-algebraic classes for the tower of Brown-Peterson spectra.