Homology, Homotopy and Applications

Volume 19 (2017)

Number 1

Comparison of power operations in Morava $E$-theories

Pages: 59 – 87

DOI: http://dx.doi.org/10.4310/HHA.2017.v19.n1.a4


Takeshi Torii (Department of Mathematics, Okayama University, Okayama, Japan)


There is a Hopf algebroid without antipode which is the dual of the algebra of power operations in Morava $E$-theory. In this paper we compare the category of comodules over the Hopf algebroid in the $n$th Morava $E$-theory with that in the $(n + 1)$st Morava $E$-theory. We show that the $n$th Morava $E$-theory of a finite complex with power operations can be obtained from the $(n + 1)$st Morava $E$-theory with power operations.


Morava $E$-theory, power operation, $p$-divisible group, Hopf algebroid

2010 Mathematics Subject Classification

14L05, 55N22, 55S25

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