Subgroups of 𝑝-divisible groups and centralizers in symmetric groups

Abstract

We give a formula relating the transfer maps for the cohomology theories E n E_{n} and C t C_t to the transchromatic generalized character maps of a previous paper by the author. We then apply this to understand the effect of the transchromatic generalized character maps on Strickland’s isomorphism between the Morava E E -theory of the symmetric group Σ p k \Sigma _{p^k} (modulo a transfer ideal) and the global sections of the scheme that classifies subgroups of order p k p^k in the formal group associated to E n E_{n} . This provides an algebro-geometric interpretation to the C t C_t -cohomology of the class of groups arising as centralizers of finite sets of commuting elements in symmetric groups.