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 F p . 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 F p 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.

中文翻译：

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形式变形水平结构下降的范数相干性

摘要 我们给出了形式群变形的层次结构的下降公式，并研究了下降与规范构造之间的兼容性。在这个框架下，我们概括了 Ando 在 F p 上为与 Honda 形式群相关的 Morava E 理论构建的 H ∞ 复方向。我们展示了与 F p 代数扩展上的正式群相关的任何 Morava E 理论的这种取向的存在性和唯一性，特别是椭圆上同调理论家族的取向。这些方向对应于形式群的变形坐标，这些坐标与沿下降的范数图兼容。