The congruence criterion for power operations in Morava E-theory

We prove a congruence criterion for the algebraic theory of power operations in Morava E-theory, analogous to Wilkerson’s congruence criterion for torsion free lambda-rings. In addition, we provide a geometric description of this congruence criterion, in terms of sheaves on the moduli problem of deformations of formal groups and Frobenius isogenies.