## Subgroups of $p$-divisible groups and centralizers in symmetric groups

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- by Nathaniel Stapleton PDF
- Trans. Amer. Math. Soc.
**367**(2015), 3733-3757 Request permission

## Abstract:

We give a formula relating the transfer maps for the cohomology theories $E_{n}$ and $C_t$ 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 $E$-theory of the symmetric group $\Sigma _{p^k}$ (modulo a transfer ideal) and the global sections of the scheme that classifies subgroups of order $p^k$ in the formal group associated to $E_{n}$. This provides an algebro-geometric interpretation to the $C_t$-cohomology of the class of groups arising as centralizers of finite sets of commuting elements in symmetric groups.## References

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## Additional Information

**Nathaniel Stapleton**- Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
- Received by editor(s): June 4, 2013
- Received by editor(s) in revised form: November 8, 2013
- Published electronically: December 10, 2014
- © Copyright 2014 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**367**(2015), 3733-3757 - MSC (2010): Primary 55N20, 55N22; Secondary 14L05
- DOI: https://doi.org/10.1090/S0002-9947-2014-06344-7
- MathSciNet review: 3314822