Realizability of the Adams-Novikov spectral sequence for formal $A$-modules

Abstract

We show that the formal A-module Adams-Novikov spectral sequence of Ravenel does not naturally arise from a filtration on a map of spectra by examining the case A = Z[i]. We also prove that when A is the ring of integers in a nontrivial extension of Qp, the map (L, W) → (L A , W A ) of Hopf algebroids, classifying formal groups and formal A-modules respectively, does not arise from compatible maps of E ∞ -ring spectra (MU, MU^MU)→ (R, S).