Transchromatic generalized character maps

Abstract

The generalized character map of Hopkins, Kuhn, and Ravenel [J. Amer. Math. Soc. 13 (2000) 553–594] 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 $E$. We use the language of $p$–divisible groups to construct extensions of the generalized character map for Morava $E$–theory to every height between $0$ and $n$.