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The character of the total power operation

Tobias Barthel and Nathaniel Stapleton

Geometry & Topology 21 (2017) 385–440

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(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 GLn(p)–invariant generalized class functions is a natural transformation of global power functors on finite groups.

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power operations, generalized character theory, Morava $E$–theory
Mathematical Subject Classification 2010
Primary: 55N22, 55S25
Secondary: 55P42
Received: 26 February 2015
Revised: 26 September 2016
Accepted: 15 January 2016
Published: 10 February 2017
Proposed: Haynes Miller
Seconded: Mark Behrens, Jesper Grodal
Tobias Barthel
Department of Mathematical Sciences
University of Copenhagen
Universitetsparken 5
DK-2100 Copenhagen
Nathaniel Stapleton
Fakultät für Mathematik
Universität Regensburg
D-93040 Regensburg