A Tannakian framework for G-displays and Rapoport-Zink spaces

2019/06/03 by Patrick Daniels, Daniels, Patrick · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1906.00899

openalex publication_date 2019/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop a Tannakian framework for group-theoretic analogs of displays, originally introduced by Bültel and Pappas, and further studied by Lau. We use this framework to define Rapoport-Zink functors associated to triples (G,\μ\,[b]), where G is a flat affine group scheme over ℤ_p and μ is a cocharacter of G defined over a finite unramified extension of ℤ_p. We prove these functors give a quotient stack presented by Witt vector loop groups, thereby showing our definition generalizes the group-theoretic definition of Rapoport-Zink spaces given by Bültel and Pappas. As an application, we prove a special case of a conjecture of Bültel and Pappas by showing their definition coincides with that of Rapoport and Zink in the case of unramified EL-type local Shimura data.

Cited by

• The Shimurian BT stack is a gerbe over truncated displays
• Ring stacks conjecturally related to the stacks BT_n^G,μ

Related

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• Rapoport-Zink Spaces For Local P-Shtukas and Their Local Models
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• G-displays of Hodge type and formal p-divisible groups