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arXiv · 1502.01987

The character of the total power operation

Tobias Barthel·Nathaniel Stapleton
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Abstract

In this paper 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 Drinfeld 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.

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Tobias Barthel, Nathaniel Stapleton. 2015-02-06. The character of the total power operation. https://doi.org/10.2140/gt.2017.21.385

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