The action of the automorphisms of a formal group on its deformation space is crucial to understanding periodic families in the homotopy groups of spheres and the unsolved Hecke orbit conjecture for unitary Shimura varieties. This action is called the Lubin-Tate action. We first show sufficient conditions for geometrically modelling this action as coming from an action on a moduli stack, generalizing previous constructions using the moduli stack of elliptic curves. We then construct such a stack satisfying these conditions for height p-1 for all odd primes p, and conjecture the correct stack for height h=p^{k-1}(p-1) for all odd primes. These heights capture all topologically interesting information for odd primes. We construct these stacks both locally and globally using inverse Galois theory and Hurwitz stacks. Finally, we relate these stacks to the reduced regular representation of cyclic groups, and use this to compute the action explicitly.

Creator

• Ray, Catherine

DOI

• https://doi.org/10.21985/n2-3qsk-km67

Subject

• Mathematics

Language

• en

Alternate Identifier

• etdadmin_upload_1013588
• http://dissertations.umi.com/northwestern:16756

Keyword

• algebraic geometry
• homotopy theory
• arithmetic geometry

Date created

• 2023-01-01

Resource type

• Dissertation

Rights statement

• In Copyright