Comparison of power operations in Morava $E$-theories

摘要

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.