The character of the total power operation

Tobias Barthel; Nathaniel Stapleton

doi:10.2140/gt.2017.21.385

The character of the total power operation

Tobias Barthel, Nathaniel Stapleton

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We compute the total power operation for the Morava E-theory of any finite group up to torsion. Our formula is stated in terms of the GL_n (ℚ_p)-action on the Drinfel’d ring of full level structures on the formal group associated to E-theory. It can be specialized to give explicit descriptions of many classical operations. Moreover, we show that the character map of Hopkins, Kuhn and Ravenel from E-theory to GL_n(ℤ_p)-invariant generalized class functions is a natural transformation of global power functors on finite groups.

Original language	English
Pages (from-to)	385-440
Number of pages	56
Journal	Geometry and Topology
Volume	21
Issue number	1
DOIs	https://doi.org/10.2140/gt.2017.21.385
State	Published - Feb 10 2017

Bibliographical note

Publisher Copyright:
© 2017, Mathematical Sciences Publishers. All rights reserved.

Keywords

Generalized character theory
Morava E-theory
Power operations

ASJC Scopus subject areas

Geometry and Topology

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10.2140/gt.2017.21.385

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AB - We compute the total power operation for the Morava E-theory of any finite group up to torsion. Our formula is stated in terms of the GLn (ℚp)-action on the Drinfel’d ring of full level structures on the formal group associated to E-theory. It can be specialized to give explicit descriptions of many classical operations. Moreover, we show that the character map of Hopkins, Kuhn and Ravenel from E-theory to GLn(ℤp)-invariant generalized class functions is a natural transformation of global power functors on finite groups.

KW - Generalized character theory

KW - Morava E-theory

KW - Power operations

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EP - 440

JO - Geometry and Topology

JF - Geometry and Topology

IS - 1

ER -

The character of the total power operation

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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