Subgroups of p-divisible groups and centralizers in symmetric groups

TL;DR

This paper offers an algebraic geometric interpretation of the cohomology of certain groups related to Morava E-theory, focusing on centralizers in symmetric groups and subgroup schemes of p-divisible groups.

Contribution

It introduces a novel geometric perspective on the cohomology of centralizer groups in symmetric groups using subgroup schemes of p-divisible groups.

Findings

Provides an interpretation of cohomology via connected components of schemes

Links group cohomology to algebraic geometry of p-divisible groups

Enhances understanding of group structures in algebraic topology

Abstract

For cohomology theories closely related to Morava E-theory, we provide an algebro-geometric interpretation of the cohomology of groups that arise as centralizers of tuples of commuting elements inside of symmetric groups. The interpretation is given in terms of the connected components of the scheme that classifies subgroup schemes of a particular p-divisible group.