The Moduli Stack of Breuil-Kisin Modules with Descent Data for Reductive Groups

We introduce and study the moduli stack Y of Breuil-Kisin modules with Ĝ-structure and descent data, or Breuil-Kisin (Γ,Ĝ)-torsors for short. Specifically, for a dominant cocharacter μ, we define the moduli stack Y≤ μ of Breuil-Kisin (Γ,Ĝ)-torsors with Hodge-Tate weights bounded by μ. We prove that Y≤ μ is a p-adic formal algebraic stack, and show that it is smoothly equivalent to (the p-adic completion of) a twisted Schubert variety Gr≤ μG in the sense of Pappas-Zhu. This is a reformatted and lightly edited version of the author's PhD thesis, submitted to Northwestern University in August 2024.