The character of the total power operation

Barthel, Tobias¹ ; Stapleton, Nathaniel²

¹ Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark
² Fakultät für Mathematik, Universität Regensburg, D-93040 Regensburg, Germany

Geometry & topology, Tome 21 (2017) no. 1, pp. 385-440.

Résumé

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 ${GL}_n\left({\mathbb{Q}}_p\right)$–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 ${GL}_n\left({\mathbb{Z}}_p\right)$–invariant generalized class functions is a natural transformation of global power functors on finite groups.

Détail

DOI : 10.2140/gt.2017.21.385

Classification : 55N22, 55S25, 55P42
Keywords: power operations, generalized character theory, Morava $E$–theory

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