A canonical lift of Frobenius in Morava E-theory

Stapleton, Nathaniel

doi:10.4310/HHA.2019.v21.n1.a16

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A canonical lift of Frobenius in Morava E-theory

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Stapleton, Nathaniel
Max Planck Institute for Mathematics, Max Planck Society;

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http://dx.doi.org/10.4310/HHA.2019.v21.n1.a16
(Publisher version)

https://doi.org/10.48550/arXiv.1603.04811
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Citation

Stapleton, N. (2019). A canonical lift of Frobenius in Morava E-theory. Homology, Homotopy and Applications, 21(1), 341-350. doi:10.4310/HHA.2019.v21.n1.a16.

Cite as: https://hdl.handle.net/21.11116/0000-0003-D42C-D

Abstract

We prove that the $p$th Hecke operator on the Morava $E$-cohomology of a space is congruent to the Frobenius mod $p$. This is a generalization of the fact that the $p$th Adams operation on the complex $K$-theory of a space is congruent to the Frobenius mod $p$. The proof implies that the $p$th Hecke operator may be used to test Rezk's congruence criterion.