Transchromatic generalized character maps

TL;DR

This paper extends the concept of generalized character maps in complex oriented cohomology theories to include landing in all intermediate heights between 0 and n, using p-divisible groups.

Contribution

It generalizes the existing character map construction for Morava E-theory to encompass all heights t between 0 and n, utilizing p-divisible groups.

Findings

Constructed generalized character maps for all heights t

Extended the framework to include intermediate cohomology theories

Provided new tools for studying cohomology rings of classifying spaces

Abstract

In "Generalized Group Characters and Complex Oriented Cohomology Theories", Hopkins, Kuhn, and Ravenel develop a way to study cohomology rings of the form E^*(BG) in terms of a character map. The character map can be interpreted as a map of cohomology theories beginning with a height n cohomology theory E and landing in a height 0 cohomology theory with a rational algebra of coefficients that is constructed out of E. In this paper we use the language of p-divisible groups to extend their construction for Morava E-theory so that the character map can land in every height t between 0 and n.