Number Theory Seminar

Speaker: Zachary Gardner

Title: Moduli of (𝒢, μ)-Apertures

Abstract: Fix a prime p and let 𝒢 be a smooth affine Z_p-group scheme and μ a 1-bounded cocharacter of 𝒢. Given n≥1, we study the moduli stack BT_n^𝒢,μ of (𝒢,μ)-apertures of level n built using the notion of syntomification recently introduced by Bhatt-Lurie. We show that this stack serves as a group-theoretic generalization of the moduli stack of n-truncated p-divisible groups (with prescribed height and dimension), with analogous smoothness, finiteness, and representability properties and satisfying analogues of Dieudonne theory and Grothendieck-Messing theory. As time allows, we will explain how these results fit into a more general formalism with broader applications in arithmetic geometry and homotopy theory. This is joint work with Keerthi Madapusi.

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