Ravenel-type classification of the classes generated by BP quotients

Establish whether the cohomological Bousfield classes of $BP/J$ and $BP/K$ in $L_{\HFp}$ are equal if and only if the invariant regular sequences $J$ and $K$ are equivalent under Ravenel’s relation $\sim$.

Background

The paper considers cohomological Bousfield classes generated by quotients $BP/J$ associated to infinite invariant regular sequences. It recalls Ravenel’s conjecture that equality of the corresponding Bousfield classes is characterized exactly by the equivalence relation on sequences, and then adopts the same assertion as a conjecture in the present setting. If true, the result would imply that $L_{\HFp}$ contains uncountably many cohomological Bousfield classes that are not homological.