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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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.
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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