Level structures on $p$-divisible groups from the Morava $E$-theory of abelian groups

TL;DR

This paper investigates the connection between level structures on certain $p$-divisible groups and Morava $E$-cohomology of iterated free loop spaces of classifying spaces of finite abelian groups, advancing understanding in algebraic topology.

Contribution

It explores the relationship between level structures on $p$-divisible groups and Morava $E$-cohomology of loop spaces, extending previous work on formal groups and power operations.

Findings

Established links between level structures and Morava $E$-cohomology of loop spaces.

Provided new insights into the structure of $p$-divisible groups in relation to cohomology.

Enhanced understanding of power operations in Morava $E$-theory.

Abstract

The close relationship between the scheme of level structures on the universal deformation of a formal group and the Morava $E$-cohomology of finite abelian groups has played an important role in the study of power operations for Morava $E$-theory. The goal of this paper is to explore the relationship between level structures on the $p$-divisible group given by the trivial extension of the universal deformation by a constant $p$-divisible group and the Morava $E$-cohomology of the iterated free loop space of the classifying space of a finite abelian group.