A rational approach to Hopf rings Original Research Article

We study Hopf rings of the form E*(F*), where E*(−) is a complex oriented homology theory and F* is the graded ring space arising from a complex oriented Ω-spectrum F. We propose a new model Hopf ring E*Q(F*) which is constructed by purely algebraic means from the rationalisations image, image and image, and which in many cases is isomorphic to E*(F*). Our model may be expressed in terms of the conjugate Bell polynomials associated with the exponential series for E and F, and we explain how calculations may be carried out in this context. We discuss the relationship between E*Q(F*) and the well-known model E*Q(F*) due to Ravenel and Wilson.