Deformations of Prismatic Higher $(G,\mu)$-Displays over Quasi-Syntomic Rings

Ali Partofard; Mohammad Hadi Hedayatzadeh

arxiv: 2402.12879 · v3 · submitted 2024-02-20 · 🧮 math.NT · math.AG

Deformations of Prismatic Higher (G,μ)-Displays over Quasi-Syntomic Rings

Mohammad Hadi Hedayatzadeh , Ali Partofard This is my paper

classification 🧮 math.NT math.AG

keywords prismaticringsdisplayshigherquasi-syntomicapplicationclassclassification

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We prove a deformation theorem for prismatic higher $(G,\mu)$-displays over quasi-syntomic rings. As an application, we extend the classification of $p$-divisible groups via prismatic Dieudonn\'e modules to a class of rings, properly containing quasi-syntomic rings. Finally, we relate the stack of prismatic higher $(G,\mu)$-displays to integral local Shimura varieties.

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A uniform construction of stacks BT^{G,μ}_n using stacky prismatic technology verifies Drinfeld's algebraicity conjecture and yields a linear-algebraic classification of truncated p-divisible groups over general p-adic bases.