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


Author: Nathaniel Stapleton
Journal: Trans. Amer. Math. Soc. 367 (2015), 3733-3757
MSC (2010): Primary 55N20, 55N22; Secondary 14L05
Published electronically: December 10, 2014
MathSciNet review: 3314822
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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.


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Additional Information

Nathaniel Stapleton
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

DOI: https://doi.org/10.1090/S0002-9947-2014-06344-7
Received by editor(s): June 4, 2013
Received by editor(s) in revised form: November 8, 2013
Published electronically: December 10, 2014
Article copyright: © Copyright 2014 American Mathematical Society