A Tannakian Framework for G-displays and Rapoport–Zink Spaces

Author:

Daniels Patrick1

Affiliation:

1. Department of Mathematics, University of Maryland, College Park, MD 20742, USA

Abstract

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 $(G,\{\mu \},[b])$, where $G$ is a flat affine group scheme over ${\mathbb{Z}}_p$ and $\mu$ is a cocharacter of $G$ defined over a finite unramified extension of ${\mathbb{Z}}_p$. 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.

Funder

NSF

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Reference23 articles.

1. -displays and Rapoport–Zink spaces;Bültel;J. Inst. Math. Jussieu,2017

2. Tannakian categories.;Deligne,1982

3. Frobenius gauges and a new theory of p-torsion sheaves in characteristic p. I;Fontaine,2013

4. Cohomologie non abélienne;Giraud,1971

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1. G-displays of Hodge type and formal p-divisible groups;manuscripta mathematica;2023-04-08

2. Higher frames and G-displays;Algebra & Number Theory;2021-12-23

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