Norm coherence for descent of level structures on formal deformations

Abstract

We give a formulation for descent of level structures on deformations of formal groups and study the compatibility between descent and a norm construction. Under this framework, we generalize Ando's construction of H∞ complex orientations for Morava E-theories associated to the Honda formal groups over Fp. We show the existence and uniqueness of such an orientation for any Morava E-theory associated to a formal group over an algebraic extension of Fp and, in particular, orientations for a family of elliptic cohomology theories. These orientations correspond to coordinates on deformations of formal groups that are compatible with norm maps along descent.