A transchromatic proof of Strickland's theorem

Tomer M. Schlank, Nathaniel Stapleton

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

In [15] Strickland proved that the Morava E-theory of the symmetric group has an algebro-geometric interpretation after taking the quotient by a certain transfer ideal. This result has influenced most of the work on power operations in Morava E-theory and provides an important calculational tool. In this paper we give a new proof of this result as well as a generalization by using transchromatic character theory. The character maps are used to reduce Strickland's result to representation theory.

Original languageEnglish
Pages (from-to)1415-1447
Number of pages33
JournalAdvances in Mathematics
Volume285
DOIs
StatePublished - Nov 5 2015

Bibliographical note

Funding Information:
It is a pleasure to thank Jacob Lurie for suggesting reduction to height 1. With a sentence he initiated this project. We would like to thank Tobias Barthel for many useful conversations and for his interest from the very start. We have been strongly influenced by the work of Charles Rezk and Neil Strickland and we are grateful to Charles Rezk for several discussions. We also thank Mark Behrens, Pavel Etingof, Tyler Lawson, Haynes Miller, Peter Nelson, Eric Peterson, and Vesna Stojanoska for their many helpful remarks. We would also like to thank the referee for helpful comments. The first author was supported by the Simons Foundation and the second author was partially supported by NSF grant DMS-0943787 .

Publisher Copyright:
© 2015 Elsevier Inc.

Keywords

  • Character theory
  • Chromatic homotopy
  • Morava E-theory

ASJC Scopus subject areas

  • Mathematics (all)

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