# Norm coherence for descent of level structures on formal deformations

## TL;DR

This paper develops a framework for descent of level structures on formal group deformations, generalizing complex orientations in Morava E-theories and elliptic cohomology through norm-compatible coordinates.

## Contribution

It introduces a norm coherence formulation for descent, extending Ando's H-infinity orientations to broader Morava E-theories and elliptic cohomology.

## Key findings

- Existence and uniqueness of orientations for Morava E-theories over algebraic extensions of F_p
- Construction of norm-compatible coordinates on formal group deformations
- Application to orientations in elliptic cohomology theories

## Abstract

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