The purpose of this talk is to describe the structure inherent in the Morava E-theory of a commutative S-algebra. Ando, Hopkins, and Strickland have shown how this structure encodes information about isogenies of deformations of a finite height formal group. We will use their work to describe the natural target category C of the functor defined by Morave E-homology whose domain category is commutative S-algebras. The answer is that C is a category of sheaves on a certain generalized stack, with a twist: the objects of C are exactly those sheaves which satisfy a certain congruence condition related to Frobenius isogenies. This answer is a precise analogue to the “Wilkerson criterion” for lambda-rings.