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A Tannakian Framework for Displays and Rapoport-Zink Spaces

By Patrick Daniels

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 Zp and μ is a cocharacter of G defined over a finite unramified extension of Zp. 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

Topics: Mathematics, displays, p-divisible groups, Rapoport-Zink spaces
Publisher: 'Wiley'
Year: 2020
DOI identifier: 10.13016/g0m2-i2ix
OAI identifier: oai:drum.lib.umd.edu:1903/26065
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