A transchromatic proof of Strickland's theorem

Tomer M. Schlank; Nathaniel Stapleton

doi:10.1016/j.aim.2015.07.025

A transchromatic proof of Strickland's theorem

Tomer M. Schlank
, Nathaniel Stapleton

Mathematics

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	1415-1447
Number of pages	33
Journal	Advances in Mathematics
Volume	285
DOIs	https://doi.org/10.1016/j.aim.2015.07.025
State	Published - Nov 5 2015

Bibliographical note

Publisher Copyright:
© 2015 Elsevier Inc.

Funding

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 .

Funders	Funder number
Simons Foundation
U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China	DMS-0943787

Keywords

Character theory
Chromatic homotopy
Morava E-theory

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1016/j.aim.2015.07.025

Cite this

@article{a3ad4b09d71e44168921d022823a5993,

title = "A transchromatic proof of Strickland's theorem",

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.",

keywords = "Character theory, Chromatic homotopy, Morava E-theory",

author = "Schlank, \{Tomer M.\} and Nathaniel Stapleton",

note = "Publisher Copyright: {\textcopyright} 2015 Elsevier Inc.",

year = "2015",

month = nov,

day = "5",

doi = "10.1016/j.aim.2015.07.025",

language = "English",

volume = "285",

pages = "1415--1447",

}

TY - JOUR

T1 - A transchromatic proof of Strickland's theorem

AU - Schlank, Tomer M.

AU - Stapleton, Nathaniel

PY - 2015/11/5

Y1 - 2015/11/5

N2 - 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.

AB - 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.

KW - Character theory

KW - Chromatic homotopy

KW - Morava E-theory

UR - https://www.scopus.com/pages/publications/84941236275

UR - https://www.scopus.com/pages/publications/84941236275#tab=citedBy

U2 - 10.1016/j.aim.2015.07.025

DO - 10.1016/j.aim.2015.07.025

M3 - Article

AN - SCOPUS:84941236275

SN - 0001-8708

VL - 285

SP - 1415

EP - 1447

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

A transchromatic proof of Strickland's theorem

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this